I think rooming with a stranger is scary man or woman, I recently took a singles cruise and got very lucky with a great cabin mate of the same sex., though she was married. Singles cruise groups will NOT room you with a woman, they would only look for a same sex roomate for you due to liabilty reasons.
My advice is try a man or go alone, but book with a singles group, if your social you should at least make some friends,
(many people who take these are people who simply don't want to be alone on vacation, they may be in a relationship but their partner can't travel or does not enjoy it, some are not necessarily looking for romance, though some are)
If you talk to people and socialize hopefully you will meet a lady friend who in the future would be willing to travel with you. As for me I meet a bunch of nice people on my singles cruise, our group bonded quickly and I always ran into them all over the ship, I was seldom without company. Now we are keeping in touch via e mail, and I hope to see them again on a future trip. As for rooming with a man, you really don't hang out too much in your cabin on a cruise (way too much to do elsewhere) so I say give it a shot, unless you can afford the singles supplement.