Mounting Speakers On A Furniture Dolly For Mobility

It will affect the sound. Everything matters. Will it deteriorate enough to negate the utility you require? Probably not. You might add a more suitable platform on the dolly, like a paving slab.

If you have to move them then you have to move them.

The biggest consideration for these setups is to make sure that there is no rocking of the speaker at all.  You want to be able to press on the top front to back and make sure there is zero tilting going on.  Also, you do want to use locking casters.

Also look at low profile platforms. Some have feet for stability. 

Unfortunately most speakers come with spikes and there are many specialty products like Podiums that significantly improve the sound even more. Using furniture dolly’s will have a performance hit… probably a pretty big one. 
 

Could you bribe your wife with a diamond braclet or something to leave them in their best position… which typically takes days or weeks of experimentation to find and 1/4” can sometimes make a large difference.