Definitely pay a gunsmith or send it to S&W but, depending on how close the replacement barrel fits, expect to pay $80 to $160. About 10 years ago S&W quoted me $100 including return shipping to install a barrel sent in along with the revolver but it was going to cost $45 to ship it to them by private carrier. I got lucky once. Without lathe work a used replacement barrel screwed in until the sight was straight up with correct torque and the B/C gap within specification. The gap was only a couple thousands larger than ideal. I had been using the smith regularly. He charged me $35. That is rare. Lathe turning is normally part of installing S&W revolver barrels. Not all barrels fit inside the lathe's 4 jaw chuck. Those that do not have to be set up between the chuck and a live center. My guess is a 3 1/2" Model 27 barrel would have to be set up outside of the chuck. That takes more time.
Not all local smiths have frame wrenches made for specific revolver frames. Some have made their own more or less universal frame wrenches that work fine if the old barrel is not on especially tight but are questionable if it is extra tight. Many young gunsmiths have mostly worked on simi-automatics. I suggest finding a gunsmith with grey hair and professionally made frame wrenches or sending it to S&W.
Also shop carefully when buying used barrels. When damaged barrels are removed they seldom get tossed in the trash where they belong. They usually go in the smith's junk box which eventually winds up in someone else's hands. Then the barrels get sold on eBay as good barrels. You might not know what's wrong with one until your smith examines it so take a used barrel to him in time for it to be returned to the seller.
