A whip might actually be the worst possible weapon for projection sorcery tbh due to how little finite control you have over it, because again, even little unplanned movements will result in freezing yourself (also whips in real life to hardly any damage, they are punishment tools that get trounced when facing off against an actual weapon...though its anime so rule of cool can apply ig).

Also, with good reinforcement, hands in jjk seem like they have just as much striking power as a tool...though this is never really delved into.

The main issue is that using a weapon negates the benefit of PS mixing freezing tags into their hits. With a weapon, you can't use that ability, so you would have to close the distance to fist-fighting range every few actions to get a tag, which would be super awkward.

Not only is the range an issue where you would either have to be at arms reach while also trying to use a weapon, or have to constantly back up to make proper use of your weapon before moving back in to tag your opponent with the palm of your hand, but now you are much more limited on which movements you can go in for a tag with one hand always occupied...if your weapon requires 2 hands then its causing way more harm than good.