You'll need a barrel vise and an action wrench.

I would not put that wrench on an action that it isn't configured to fit, and I wouldn't put the barrel into a bench vise with or without blocks.

I guess you could apply "Trinidad Torque" using a honking huge, heavy crescent wrench on the action wrench, and giving it a healthy swing.  Another way is to put a scale on the handle to measure the torque, or a weight on the handle to apply the final torque up..

You'll also need headspace gauges and a plan about what to do if the new barrel doesn't head space correctly.

The installation torque can be broken with a big dead blow hammer while applying torque.  The hammer blow helps by breaking friction in the threads, plus applying a torque via impulse on the handle.

Not an internal wrench, one that won't crush the action and fits the outer diameter tight so it won't slip.

I guess all you can do is give it a try.  I don't know if the Tikka action has a flat bottom.