The three Avicularia I've handled (one a versicolor) all move lightning fast in the cage, but seem to slow down quite a bit when being handled, and take a more 'let me check this place out' type of additude. I wouldn't worry too much about moving one, I got a little paranoid with my first one being so small and fast, but have since taken it out a few times to be handled, and can in good faith say, that if you're gentle, and have your wits about you, there's no reason you shouldn't be able to simply coax it from one container to the next, with a soft paintbrush.
If you plan on handling your Versi, it is never too late to start. I have had many Avic. slings that will come out of their container when I open it up to feed them. Once you toss in the crickets and spray the container, just coax it back in. You should be able enjoy the sling and get use to holding it ( if you want to!!)