The grinder weighs close to 35 lbs, which is at the upper limit of the side shelf. It's a slow speed wet grinder so you don't push hard. The mechanic's carts have 2 locking wheels which should be more than enough to stop it from moving. It doesn't turn fast enough to worry about vibrating or walking.
This is a Tromek grinder. It turns at about 100 rpm, very slow and the wheel sits in a water tray so the wheel is always wet. The wheel has, nor does it need a guard like a regular grinder. You can reshape a tool on it but it would like watching grass grow. You don't push hard on it so the rubber feet are more than enough to keep it from moving. Because there's no guard you can grind on either side of the wheel so either you need to be able to have access to both sides or be able to turn it around easily. With the optional diamond wheel you can even grind on the side of the wheel. The smaller tray would need to have something larger attached to it as it's smaller than the footprint of the grinder.
I did a search but didn't see the coupon for the 4 drawer cart.