It would be interesting to know why do you think you need extra server - do you actually have a bottle neck for generating the cookie or somewhere else ? Is it the log writing as requests happen alot ? ajax polling ? Client download speed ?
Atleast for starters, i'd look something more efficient than fetching time to generate the "random hash". For example, on this intel i7 laptop i have, generating 999999 md5 hashes from microtime takes roughly about 4 seconds and doing same thing with random numbers is second faster (not taking a seeding of rand into account).
Then, if you take opening/and closing of socket into account, just moving your script (which is most likely already really fast - that is, without knowing how your pages take that into account), you will end up actually slowing down the requests. Actually, now that i've re-read your question, it makes me think that your cookie setter script is already a dedicated page ? Or do you just "include" into real content served by another php script? If not, try that approach. Also this would beneficial if you have default logging rules for apache, if cookies are set in on own page, your apache will log a row for that and in high load systems, this will cumulate to total io time spend by apache.
Also, consider that testing if cookie is set and then setting it, might be slower than just to forcefully set it always even if cookie exists or not ?
But overall, i don't think you'd need to set up a server just to offload cookie generation without knowing more about how you handle the cookies now.. Unless you are doing something really nasty.