Of course you can create some external object providing an equality comparison and a HashCode. But the build-in collections of Java do not use such an object for their comparisons/lookup.
I once did create an interface like this in my package-collection (just freshly translated to english):
public interface HashableEquivalenceRelation {
    /**
     * Returns true if two objects are considered equal.
     *
     * This should form an equivalence relation, meaning it
     * should fulfill these properties:
     *  <ul>
     *    <li>Reflexivity:  {@code areEqual(o, o)}
     *            should always return true.</li>
     *    <li>Symmetry: {@code areEqual(o1,o2) == areEqual(o2,o1)}
     *            for all objects o1 and o2</li>
     *    <li>Transitivity: If {@code areEqual(o1, o2)} and {@code areEqual(o2,o3)},
     *            then {@code areEqual(o1,o3}} should hold too.</li>
     *  </ul>
     * Additionally, the relation should be temporary consistent, i.e. the
     * result of this method for the same two objects should not change as
     * long as the objects do not change significantly (the precise meaning of
     * <em>change significantly</em> is dependent on the implementation).
     *
     * Also, if {@code areEqual(o1, o2)} holds true, then {@code hashCode(o1) == hashCode(o2)}
     * must be true too.
     */
    public boolean areEqual(Object o1, Object o2);
    /**
     * Returns a hashCode for an arbitrary object.
     *
     * This should be temporary consistent, i.e. the result for the same
     * objects should not change as long as the object does not change significantly
     * (with change significantly having the same meaning as for {@link areEqual}).
     *
     * Also, if {@code areEqual(o1, o2)} holds true, then {@code hashCode(o1) == hashCode(o2)}
     * must be true too.
     */
    public int hashCode(Object o);
}
Than I had a group of interfaces CustomCollection, CustomSet, CustomList, CustomMap, etc. defined like the interfaces in java.util, but using such an equivalence relation for all the methods instead of the build-in relation given by Object.equals. I had some default implementations, too:
/**
 * The equivalence relation induced by Object#equals.
 */
public final static EquivalenceRelation DEFAULT =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2)
        {
            return
                o1 == o2 ||
                o1 != null &&
                o1.equals(o2);
        }
        public int hashCode(Object ob)
        {
            return
                ob == null?
                0 :
                ob.hashCode();
        }
        public String toString() { return "<DEFAULT>"; }
    };
/**
 * The equivalence relation induced by {@code ==}.
 * (The hashCode used is {@link System#identityHashCode}.)
 */
public final static EquivalenceRelation IDENTITY =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2) { return o1 == o2; }
        public int hashCode(Object ob) { return System.identityHashCode(ob); }
        public String toString() { return "<IDENTITY>"; }
    };
/**
 * The all-relation: every object is equivalent to every other one.
 */
public final static EquivalenceRelation ALL =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2) { return true; }
        public int hashCode(Object ob) { return 0; }
        public String toString() { return "<ALL>"; }
    };
/**
 * An equivalence relation partitioning the references
 * in two groups: the null reference and any other reference.
 */
public final static EquivalenceRelation NULL_OR_NOT_NULL =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2)
        {
            return (o1 == null && o2 == null) ||
                (o1 != null && o2 != null);
        }
        public int hashCode(Object o) { return o == null ? 0 : 1; }
        public String toString() { return "<NULL_OR_NOT_NULL>"; }
    };
/**
 * Two objects are equivalent if they are of the same (actual) class.
 */
public final static EquivalenceRelation SAME_CLASS =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2)
        {
            return o1 == o2 || o1 != null && o2 != null &&
                o1.getClass() == o2.getClass();
        }
        public int hashCode(Object o) { return o == null ? 0 : o.getClass().hashCode(); }
        public String toString() { return "<SAME_CLASS>"; }
    };
/**
 * Compares strings ignoring case.
 * Other objects give a {@link ClassCastException}.
 */
public final static EquivalenceRelation STRINGS_IGNORE_CASE =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2)
        {
            return o1 == null ?
                o2 == null :
                ((String)o1).equalsIgnoreCase((String)o2);
        }
        public int hashCode(Object o)
        {
            return o == null ? -12345 : ((String)o).toUpperCase().hashCode();
        }
        public String toString() { return "<STRINGS_IGNORE_CASE>"; }
    };
/**
 * Compares {@link CharSequence} implementations by content.
 * Other object give a {@link ClassCastException}.
 */
public final static EquivalenceRelation CHAR_SEQUENCE_CONTENT =
    new EquivalenceRelation() {
        public boolean areEqual(Object o1, Object o2) 
        {
            CharSequence seq1 = (CharSequence)o1;
            CharSequence seq2 = (CharSequence)o2;
            if (seq1 == null ^ seq2 == null) // nur eins von beiden null
                return false;
            if (seq1 == seq2)   // umfasst auch den Fall null == null
                return true;
            int size = seq1.length();
            if (seq2.length() != size)
                return false;
            for (int i = 0; i < size; i++)
                {
                    if (seq1.charAt(i) != seq2.charAt(i))
                        return false;
                }
            return true;
        }
        /**
         * Entrspricht String.hashCode
         */
        public int hashCode(Object o)
        {
            CharSequence sequence = (CharSequence)o;
            if (sequence == null)
                return 0;
            int hash = 0;
            int size = sequence.length();
            for (int i = 0; i < size; i++)
                {
                    hash = hash * 31 + sequence.charAt(i);
                }
            return hash;
        }
    };