I mainly work on switch barrel set ups with Winchester Model 70's & Remington 700's.
I don't have a lot of knowledge regarding Tikka actions, but if they are set up to feed from the action rails, then they will need to be opened up to suit the larger cartridge.
The follower may also need to be changed and I hear that the mag boxes on Tikka's are very short, shorter than 3.4" as most standard actions measure, besides Remingtons.
A lot of my clients often have the same idea as you, but soon realise that buying a CHEAP donor, rebarreling and truing the action often ends up the same price or a little cheaper.
I have done this a few times on Howa 1500 actions and Vanguards. It works out quite affordable for them.
Food for thought.
Cheers.