I understand it might be an embarassing thought, but apparently not knowing how to swim is alarmingly common in some countries. I live on an island so I can't recall meeting someone who didn't know how to swim, but that is entirely down to geography. I think if you headed into your local pool and asked about it they'd be happy to give you the basic lessons. You'll pick up on it very quickly I bet, given you have experience already. Maybe a couple of lessons over two/three weeks to get instruction on the movements then you'll be practicing and improving on your own.
I definitely think you should go for it!