Since no one has replied.. I will..
I have the dremel multi pro. It's getting up there in years, it's corded, but I really like it. 10 speeds, more power than I'd ever need for doggie purposes. But it was gotten as a tool long before we had puppers. I keep it in the house, but it still goes out and I use it for it's real purpose. I actually inscribed a metal crate tag for Smudge with mine last year with an etching attachment.
The cord is pretty long. It's never gotten in the way. As convinient as cordless can be, we have enough tools around here that even though we properly drain them to prevent build up of memory on the battery, eventually they all have less and less charge. I'm reluctant to buy things that are cordless even with the best newest battery technology as I like my tools and don't want them to prematurely kick it for usefulness.