You want a good idea..
I’m not familiar with the snap on cart you have - but i’ll assume its a cart that doesnt have a folding lid? Either way this would still work..
Pick out the vice you want. A regular bolt on vice, whatever size you feel you need. Mount the vice onto a larger square peice of 3/4” plywood. (Say 1/3 or 1/2 the size of the top of your cart). Then go to Home Depot, or Harbor freight - and buy 4 or 5 round 30 or 60 pound pull magnets.. they have 90 pound also, but thats gonna be too much. depending on the size you make the plywood base, screw or bolt a magnet under it on all 4 corners. If you make the base big (size of the carts top) you can even place one in the center to avoid having any flex in the plywood. The plywood will let you mount the vice to the top, the magnets underneath, and give you a protective surface for the top of the cart. You can even place a layer of electrical tape on the magnets if you wanna avoid scratching the cart.
You can leave the whole thing on the cart, if you make the plywood small enough, you can remove it and hang if off the side or back of the cart with the same magnets. Granted - dont guy buying a giant vice..
I made this years ago for work.. theres 4 90lb magnets by the charger, (2 on the corners, 2 in the middle), and 2 60lb magnets on the corners by the flashlights. This things hangs VERTICALLY on a metal filing cabinet, and has not moved or slid from where i placed it in years. I actually almost hurt my fingers hanging it on caused it pulled so hard once it got close. There’s 2 9.0 batteries on in and 4 5.0 batteries today. It handles everyone pulling batteries on and off without any movement. You REALLY have to want to get this thing off for it to move. Something similar with a small vice would be no problem at all to hang off the back /side of a tool cart for storage. If you left it on the lid then all the magnets have to do is keep it from sliding.. no holes in the cart to mount anything, and it ain’t gonna move.
This way, you can get any cheap swivel base vice you want, like this one, and quickly and easily take it on and off, still store in on the side of the cart, and have a sacrificial top to cover the cart
Zerone Bench Vices,4" Mechanic Bench Vise Heavy-Duty 360° Swivel Base Table Top Clamp Bench Vice Workshop Clamp Engineers 110mm Jaw Workshop
https://www.amazon.com/dp/B07CHQNW2C/?tag=atomicindus08-20