For the past 5 years (since 2007) Unit 23 for antelope in Wyoming has been 100% draw in both the regular and special draw. In fact usually only 1/3 of the tags go to applicants who put in for that hunt for their first choice, so it looks like you would have a tag locked up. Save your money and apply for the "regular" license, don't spend the extra money on a "special" license (only used to get you better draw odds in tough to draw units).
For example, last year (2011) in Unit 23 there were approximately 1900 licenses in the regular non resident draw and a total of 535 first choice applicants.
I've never hunted for does in Wyoming, but I would assume in a unit with 100% draw for bucks, getting doe tags will not be a problem at all.