Wear whatever you feel comfortable in, but is still sensible. I see nothing wrong with a strapless bikini...
If you're skinny, and if you have just a little bit of boobs, or a correctly sized top, then I think it would be perfectly fine to wear that bikini. As long as you feel confident. Otherwise, I really would suggest the one piece. And if you do hate that one that much maybe you can look up a diy on youtube on how to cut out the sides evenly and correctly to make it a cuter one piece, and somewhat stylish.