Something that light probably wouldn't give you too much issue with recoil. The factory lugs are aluminum, which over time may deform. Steel lugs are available and are fairly inexpensive. To change them out, iirc you just grab some pliers and pull the old one, then insert the new one in it's slot.

Keep in mind that the 7mm-08 is a necked down .308 case to accept the 7mm bullet. Velocities will be appropriately slower, and nowhere near the speeds of the 7mm Rem Mag.

That said, recoil will also be appreciably less. Shouldn't have a problem on elk with proper shot placement.

I changed my lug on the recommendation from Robert at Mountain Tactical (Tikka Performance Store).  It changed the shape of the groups a little by making them stack a little more then making triangles. However, as he told me after about 300 rounds there was a small dent in the factory lug from recoil.  I'm new to Tikka as well but will change every one in the future.  The one from Mountain Tactical fit great and was not expensive at all.