Don’t worry about being embarrassed
Take it from a guy. It is extremely difficult to approach a guy and have him embarrass you.
See, most likely 10 out of 10 guys will be more than cool with a woman approaching them and will actually find it very attractive.
It’s really hard to locate a guy who isn’t flattered when a woman initiates a conversation with them or shows interest in them.
Even if they are taken, and can’t pursue any serious relationship with you, be sure they won’t embarrass you. The chances of that happening are just too low.
You want to get him to be attracted to you, primarily as a person, not as a sex-object, so desist from body contacts, such as holding his hand, or letting your hand rest on his shoulder for too long. Maintain eye contact, laugh and smile when it’s called for, and just generally relax. You don’t want to come across as too strong.