If I were you I would think VERY hard and VERY long before I changed ANYTHING about a great performing firearm.
I'm 6'2" and quite wide so getting around in the overgrown spring turkey woods can be difficult add on to this I carry a Browning square folding turkey chair, a turkey vest and a 870 ESM with a 26" barrel and things at times can get a bit more than challenging finding my way through overgrown springtime underbrush. But my gun, my chair and my vest all work so unbelievably well I refuse to change anything about any of them. And my 98% success rate (100% shot opportunity) on spring turkeys in two different states in the last 30 years is proof I should leave well enough alone.
I do have 21", 23" and 26" barrels for my 12ga 870's both 3" and 3.5" chambers. I shot enough lead turkey shells trying to find the best shell/barrel/choke combo to pay for another 870. What I found and I have no explanation as to why, but consistently my 26" barrels gave significantly better patterns from 45 yards to 60+ yards than my shorter barrels but especially were better than my 21" barrels.
No offence but in my opinion a 20ga 870 is already a pretty light gun to begin with and I personally again this is MY opinion don't see what you could gain by shedding literally 3 MAYBE 4 ounces and 2-3 inches could be possibly worth risking screwing up a great performing gun.
And unless you have a considerable stock pile of TSS or reload, current TSS shell prices even for 20ga are north of $12 a shell, so patterning and sighting in could become quite costly especially if your new shorter barrel is finicky and doesn't like the chokes you currently use.
As I said I'd give it a good deal of thought before I changed a great pattering gun for what is in MY OPINION minimal gain.
