And the supermoto class which is what you'd really want should place the least pressure on your wrists with sports bikes creating the most issues.
There are two possibles - one, you have a problem with lack of flexibility in your wrists or something like de quervain's tenosynovitis, carpel tunnel, etc.
The second and most likely problem is that you're not riding in the correct position and you have an instructor who doesn't seem to care about correcting this.
The correct position is simple - relax your shoulders, relax your arms, drop your elbows down so your forearms are parallel to the road surface and don't grip the bars too hard. You should be able to flap your arms like a demented chicken at any point. Most learners will tense up which means their wrists will hurt unless you get taught properly what to do regarding body position.
A cruiser is just.... it's... well..... can we convince you that a cruiser is just not for you? Or pretty much anyone who rides on UK roads?
Actually, the supermotos should have seats which allow you to move forward and back allowing you to get the best position for you or the style of riding you're adopting at the time.
The KTM Duke is also a good bike as above.