No one ever warned me about this side effect of buying a boat!

[mcmxi]

Have used an orbital Simoniz buffer for years. Works very nicely, only draw back is it is electric, battery operated weren't available back then. I believe any quality buffer would suit your needs. The choice of wax and using it under the recommended instructions is probably the most important detail.

Since I'd only be using the polisher at my house near the garage I don't see the disadvantage of an extension cord, and actually some advantages. Most that I've seen appear to be corded.

Variable speed without discrete settings might be the way to go. Some models have five or six speeds whereas the DeWalt has "infinite" speeds over a specific rpm range.