It's not a simple "plug & play" unscrew the old, screw in the new, kind of swap.

First, in a revolver there is no head spacing that involves the barrel, it's the barrel/cylinder gap spacing that needs to be set. Then there's getting the front sight indexed so it's at 12 o'clock.

Have a competent gunsmith do the swap. But if that will involving needing to ship it to one.. then between the cost of the barrel, shipping (both ways) and labor... it will probably be better to look for a trade or just sell yours and then buy another 629 with an 8-3/8 barrel. But that all depends to on just how common 8-3/8 bbl 629-4's are out there.... it's a judgment call either way that has to be made based on the circumstances for your particular locale/state.

Here in CA, finding an 8-3/8 barrel and sending the gun to have it swapped is a more likely scenario due to the rarity of finding a 629-4 period.

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Conrad
SWCA #1830 SWHF #222