[It's fine - James is there to steady him if he needs it, and once Sirius is upright, James sets the basket down.]

If it helps, I've been wondering if it's got something to do with how time's stopped here. It might get easier with age, but can it do that if we're not aging?

[That wasn't the case with apparition for James, but apparition doesn't involve becoming an animal that also isn't aging at all.]