Wingman Wheel with different power supply?
This is not a good idea. But most of the devices like  Wingman Formula Force have 
internal voltage regulators some may don't.And some are very sensitive.

Most probably it 22v one will work.
To make it more sure , more less probable of smoking things up, open the lid
and make sure there are regulators and it locally regulate it.
BTW, if it even works it would give trouble with time. 

So I can't give a clear answer for this. 

[I have done the same trick with a externally powered hard disk device, it worked !
no troubles yet. ].