I think the 629 barrels were never pinned, so you need a barrel vise and a receiver wrench shaped to fit the front of the receiver. The pinned barrels are not as tight, but you need a good hollow end punch to start the pin.
With the pinned barrels, it was often enough to clamp the barrel in the vise and use a couple of feet of 2x2 inserted in the cylinder well, but the newer guns without pins are torqued too tight for that and it could bend the frame.
Unless you feel you must DIY, you might be better sending it to one of the good shops like Cylinder and Slide.
Jim