First and foremost, thank you for your service, commitment and sacrifice.
Based on your age and the fact that you would not mind meeting a nice little hottie to enhance your cruising experience, I recommend . . . .
That you do some research before you book a singles group cruise. From what I have gathered through personal experience and internet research most of the singles cruise patrons are quite a bit older than you are. On my one and only singles cruise, there was only a half dozen or so passengers in the group who were in their 30's with the rest of the group being 45-50 or older. I don't think there were anyone in this group of 167 who was in their 20's. It was a VTG singles cruise in October which may have accounted for the age breakdown.
I recommend you book a shorter cruise (less than 7 nights). The general rule is the shorter the cruise, the younger the passengers. If you want more than 4 or 5 days of cruising, you can even book two 3, 4 or 5 day cruises back to back. Carnival or Royal Caribbean will probably give you the best time since they attract the young folks with their modest prices.
If you want to do a singles group cruise, go to the various companies' website and check out their photo galleries. That will give you the best idea of the demographics of passengers their particular company normally attracts.
7 night cruisers are a nice age mix but most of the passengers will probably be in their 35-50 age group. Anything longer than 7 nights and the age range will go up.
The Caribbean itineraries have the youngest passengers and the Europe/Hawaiian cruises probably have a more mature passenger base. (I took a Hawaiian cruise and 80+% of the passengers were over 65 and I was the only solo cruiser out of 2,600 passengers).
Good luck, and HAPPY CRUZIN'