Strictly money talking...likely not.

Let assume the best case a scenario that you can find a low mileage known good or warrantied engine and tranny from a wreck of the same generation of 960 for $1000 (PnP pricing if your are really lucky).

You then had to swap all the accessories and drop the combo into you existing car. You also need to do all the things you would be a fool not to do with the engine and tranny on a stand. Let assume those total up to about $300.

Assuming you have all the tools and all the know-how this is going to be a few hours pulling the old motor, get it home, cleaned, all new seals, timing belt, water pump, any tranny seals that need doing. Finally you can drop the combo in on new engine and tranny mounts. Then you have to hook everything up. Lets call the whole process 4 full days of work with at least 2 hours on each end where you need a helper...it would probably take me at least 50% more time because i have never done it before and am not familiar with the vehicle.

If you have to buy or rent any tools like an engine hoist or the combo is more expensive...

At the end of all that you have the second least reliable motor Volvo ever made in a car that has a lower street value than a nice 940 wagon and certainly less than a pristine 240 wagon.

Emotionally, spiritually or any other non-quantifiable measure is really up to you.