This shows where and how to convert, and if not using them on the current toon, how to send it to another of your own toons.

You CANNOT transfer it to another persons toon.

And yes, you can have a toon with maxed ships before it even plays one match.

If you end up skipping parts, the ending minute or so has some important information you should consider when doing this.

Something not in this video is also, you can do the conversions as you level your toon, and it will help level your ships faster.