If your enclosure is sturdy you don't really need to physically connect the drivers. The vibration cancelling effect will still be there. And I suppose you won't drive the speakers at enormous levels, if you are sitting next to them, working!
If you really think about welding pay attention, because heat can demagnetize the magnets (neodymium) and ferrite magnets may crack under the thermal stress. I wouldn't do the welding, though.