1s lipos these days typically have a height of 19mm or less. Add in that any chassis made since 2010ish and newer doesn't have cell cutouts, and a 4 cell NiMh pack isn't likely to fit.

I would expect the center shock on most cars to be the biggest interference.

Batteries keep coming down in price while improving in performance, so the best bet is to use a battery the car was built to use and slow it down with motor choice and throttle end points, if further slowing is needed.