I don't think it would bother any man!! Truthfully, I don't think any man would really object. You might get a lot of staring from guys, but whether you could handle this is your choice. Older men staring might freak you out. Younger boys would be simply curious. Maybe you should seek some advice from female friends. Try it on and let them say. Some of them might well be jealous and be envious!! How about your parents? Would they object? Only you can know the answer to that.
The impression of nipples from pokies is to be expected. Do you think the white is actually see through so you could see the color of your areolas too? That might be a bit much for a family beach, but would be pretty cool in private.
Even with padding an errect nipple can show at least a bit. I think it is fine but since white (white wet is the most see through)... unless your maybe at a family function. Beach and pool should be fine. I had a paddles black string bikini at 13 and had like 36C breasts no one cared, boys loved it.