I wouldn't sweat it that much. There's no reason to really push it. There are enough battle with strong willed kids, I know I have a strong willed 4 year old girl. I especially think not pushing her to participate if there is a male teacher is important. Let her know you will listen and respect her if she is uncomfortable with someone (especially a guy).
I did like the idea of a couple mornings at preschool. If you can find the right teacher it can be a great experience. It would provide the consistency, so she wouldn't constantly be adjusting to a new person. And the teacher would learn your child's personality too.
I'm not a permissive parent by any means, but I do think we need to listen to the kids and follow there lead sometimes. Of course yo know your child and situation best. If you really feel it is a battle worth picking, go for it. But I figure these classes are mainly for fun, so if they aren't being fun yet why bother. Of course if you make a rule about not swimming until she takes lessons, you shoud stick with it. And be sure to make it very concrete what you expect from her. "Doing good at swimming class" means different things to adults than it does to a four year old.
Once I punished my 4 year old for not telling me the truth. She said she had slept at nap, but I knew she hadn't. Later I realized that she thought closing her eyes and being quite meant that she had slept. Whoops.