Consider developing a generalized method to handle any snps. Then call it iteratively passing every snps column using lapply or sapply:
# GENERALIZED METHOD
proc_glm <- function(snps) {
   univariate <- glm(relevel(data$DX, "CON") ~ relevel(snps, "AA"), family = binomial)
   return(exp(cbind(OR = coef(univariate), confint(univariate))))
}
# BUILD LIST OF FUNCTION OUTPUT 
glm_list <- lapply(Data[3:426], proc_glm)
Use tryCatch in case of errors like relevel:
# BUILD LIST OF FUNCTION OUTPUT 
glm_list <- lapply(Data[3:426], function(col) 
                   tryCatch(proc_glm(col), error = function(e) e))
For building a data frame, adjust method and lapply call followed with a do.call + rbind:
proc_glm <- function(col){
  # BUILD FORMULA BY STRING
  univariate <- glm(as.formula(paste("y ~", col)), family = binomial, data = Data)
  # RETURN DATA FRAME OF COLUMN AND ESTIMATES
  cbind.data.frame(COL = col,
                   exp(cbind(OR = coef(univariate), confint(univariate)))
  )
}
# BUILD LIST OF DFs, PASSING COLUMN NAMES
glm_list <- lapply(names(Data)[3:426], 
                   tryCatch(proc_glm(col), error = function(e) NA))
# APPEND ALL DFs FOR SINGLE MASTER DF
final_df <- do.call(rbind, glm_list)