If you're doing the conversion on a M700 BDL, the action length will be the same and won't be a problem. Remington only makes two actions lengths--short and long--and the long action handles everything from the .30-06 family all the way up to the Ultra Mags, albeit with different bolt faces. The Ultra Mags have a rebated rim to allow the same bolt face as the magnums based on the belted H&H case, .534". You'll need a different magazine, but that should be about it.
The bigger question is why you would do such a thing. The 7mm Rem Mag is one of the most popular and versatile big game cartridges ever developed. It is supremely useful, and has a decent bore diameter to case capacity relationship. The 7mm RUM, on the other hand, is exactly the opposite. It is obnoxiously overbore, and has quickly developed a reputation and a barrel burner and one of the more finicky cartridges to load for. The 7mm Rem Mag will be with us for years to come, even if its belted case has fallen out of favor, because it has shown itself to be easy to load for, comfortable for most to shoot, and possessing a high degree of utility. You're not going to get much performance advantage from the RUM compared to the increased powder consumption, blast, recoil, barrel wear, and the cost in brass and powder. I'd keep the Rem Mag and ditch the RUM. In fact, the 7mm RUM is about as practical in my opinion as tits on a bull.