I'm really scared to "hold" my chinchilla, so I never really held him until he got tame...
Instead, what I mostly do is "scoop" him up... so I'm not so much grabbing him as I am supporting his weight. I find if "surround" him with my hands, in a cupping shape, it takes advantage of how chinchillas don't stay still, and he steps on my hands... then I just lift him.
I see some people have success with cushions, but my little guy chews just about anything and everything, so, no for my guy. I got one of those rabbit/chinchilla toys, it's a bunch of logs connected by wire, and I bent it into a tunnel, and he likes to hang out there... the reason for covering the cage floor is not cause they'd get their feet stuck (you'd have to cover the walls of the cage too then), but it's for them to rest their feet... imagine living in a chinchilla cage every day, without shoes. It'd hurt the soles of your feet, right?