Adding a subpanel to my existing service?

I would like to add a sub panel in my basement for my wood shop. The house has an range/stove 220v 8 gauge wire that has been disconnected that i would like to use. My question is can I use this wire? The wire is a 3 wire feed, hot hot natural with no ground. I understand that i have to unbound the natural at the sub panel and run the wires from the sub panel to the main panel. From what I have researched I need a 4 wire feed to accomplish this correctly. So would it be ok to run a separate ground wire from the sub to the main panel? this would be just like using a 4 wire feed to the sub correct? The existing wires from the stove feed are insulated so Im not trying to use a ground as a neutral or anything just trying to get the correct four wires to each panel. Would the uninsulated ground in a 4 wire feed be safer than a completely separate ground ran right next to a 3 wire feed?

The sub panel would be about 40 feet away in the basement not in another building. I also just happen to have 75 feet of 8 gauge ground wire. So if this would work i would have no need to purchase anything to run the wire.

Thanks for your help