If you cut the barrel down, you will loose the "mag" in your 7mm (velocity) and could be closer to 7mm-08 ballistics. Under 300 yards I don't think it will hurt much, but if you shoot out farther with it or are shooting larger game, it may make a bit of difference. I would not cut it down do to a cosmetic blem in the front sight. Like said before, get it to a gun smith and see about a brake or a fix to the sight.
Lets put some numbers on this question.
A Quuickload simulation shows H4350 powder in the 7mm08, IMR 7828 in the
7mm Rem Mag. (I use IMR7828 in my 26" 7mm RM Laredo with excellent results.
shooting 168 Grain Berger VLDS with SAAMI OAL and about 85% max loads:
barrel ---------22"---------26"
7mm-08----2540-------2630
7mmRM----2816-------2971
Those are ft/sec muzzle velocity. You can get higher velocities with other powders or hotter loads, but these are reasonable.
4" of barrel makes 90 fps difference for the 7mm08, and 155 fps difference for the 7mm Rem Mag, but the 7mm Rem Mag still has 186 fps higher velocity with a 22" barrel than a 7mm08 has iwth a 26" barrel.
The Rem Mag has more muzzle blast, and more recoil. With it's high muzzle pressure brake and large powder charge a short bareel with a muzzle brake on a 7mm RM will take away a lot of recoil though at the expense a lot of muzzle blast. A very lightweight 7mm Rem Mag is practical but hearing protection is a must.
One additional advantage, at least in a Rem 700, is that the 7mm Rem Mag giives more magaziine room (3.6") than the 7mm08 (2.8").
For what it's worth the 7mmRemMag gives 2549 fps with a 16" barrel and the same load as above., a bit more than the 7mm08 with a 22" barrel.