I would recommend slowly introducing the subject. Say something like, "I saw a really cool video of people doing something called tail-swimming."
Then you can slowly mention on it a bit more, until you say that you want to get a tail.

It will be difficult, but I bet that it will better once you get over that initial hurdle. Make sure to do it when you have your mom's full attention; that way you won't have to repeat yourself.
You might want to even show her a video, preferably one that shows guys in it too.

I hope that this goes well for you Carl. Just be confident, and if your mom says it's a little weird, stay calm, and don't get argumentative. Stay cheerful, and just say you think it would be cool.