If there's any bedding anywhere under the barrel, I would grind some of it off to provide clearance and then skim bed. Again, I'm talking about any bedding under the barrel. Bedding under the receiver will be fine.
It doesn't matter if you're getting the same profile. Bedding provides a line to line fit between two parts, meaning there is zero room to accommodate any size or form variation between the original barrel and the new one.
And I guarantee you that there will be a couple of thousands of an inch variation in outside diameter between your original barrel and the supposedly identical replacement. No two mass-produced parts are ever identical. In most cases that doesn't matter, but in this case it does.
If you want good enough, don't re-bed under the barrel. If you want it done right, do as I suggest.