Not sure what you mean by "shrouded bolt" but either rifle will work fine for your swap. I converted an old flat top 110I have from 30-06 to 338WM, for a while. I didn't even need to change magazines, neither will you. I had to swap bolt heads, but you will not.

All you will need is barrel and headspace gauges. The same gauges will work if you ever want to swap it back too. Also will need (if you do not have them already) is action vice or barrel vice, and barrel nut wrench.

Have fun.