I am about to move to my new house and I need to move my shop (since I
don't want the mover to touch my tools)

I understand your reluctance but consider:

You move your tools and something gets broke, you are holding the bag.

You move the tools and you, a family member or friend gets hurt, you've got
the bag.

A responsible mover with insurance or bond damages something, he pays for
it. Likewise if he a movers employee gets hurt the mover pays the doctor.

I coordinated lots of moves at my previous company the involved personal
equipment, computers, shop equipment and documents. With tons of stuff
moved we had very few problems - most with damaged computer equipment. The
mover picked up the damages immediately. Most reputable movers have to do
this because their reputation and business is at stake. Our last two local
moves were done by experienced apartment movers with zero damage. One of
their guys got bummed up and I felt bad but it had no effect on my wallet or
insurance.

Still.......I share your sentiment.

RonB