Edit: Forgot... just to be cantankerous and direct, nikko requires no particularly hard grip on nage's side. Nor does kotegaishi. Nor does yonkyo, unless you're committed to dancing on the nerve point, which is fun, but not required for the takedown. Sankyo... I'll get back to you on sankyo.
Sankyo either. I can do sankyo quite successfully when my partner's hands are twice the size of mine.
But there are many varieties of grip. Don't think about clamping your partner's wrist in a vise, think about the way you would hold a child's hand while crossing the street. Or how a child would hold *your* hand. It seems to me that *that* kind of connection is absolutely critical to successful aikido, and there's no way to learn about it if you've convinced yourself that you should *never* grip anything.