Mike:

You do not need to remove the barrel. There is a fairly simple process to follow when cleaning your musket after shooting.

First, use a bore scraper on the end of your cleaning rod to scrape all the burned powder from the base of the breech.
Using a cleaning rod with a brass jag on the end, dampen a patch with a cleaning solution of isopropyl alcohol, Murphy's oil soap and Hydrogen peroxide (equal parts each).

This will remove all the burned powder from the barrel. Repeat until the patch comes out fairly clean.

Using a small piece of surgical tubing about 2 feet long, a diameter which will fit over the nipple, place the tubing on the nipple. wrap a towel around the top part of the musket where you hold it, to keep excess water from going in to your stock and barrel area. Insert the other end of the tubing into a bucket of water. Wet a patch, and use the cleaning rod to push patch to the breech. Then slowly draw out the rod, sucking water through the nipple and bolster, till the rod comes most of the way out...repeat 10 or 12 times...this will further clean the barrel.

Then, remove the nipple from the bolster, and using a dental pick, scrape out all the build-up from the nipple base, and in the bolster (you may want to remove the clean out screw at this time, and use the head of a qtip with the cotton pulled off).

Dry all areas of lock and bolster, and using a good lubricant/sealer, coat all areas of nipple, threads, and bolster, and replace nipple. Then using the cleaning rod, wet a patch with Ballistol and run 2 or 3 patches (wet with lube) through the barrel.
Be sure to COMPLETELY dry all areas of your musket, and coat all metal surfaces with Ballistol. Do not use tompion in barrel, these tend to draw moisture. Springfiled will rust up if you even look at them sideways.

Good Luck!