Converting a 300WM to 257Wby

[mtelkhntr78]

I have a 300 Win mag that has a burnt out barrel. The rifle is a Model 70 and I was thinking of putting a new barrel on it. Except this time I was thinking of getting a barrel for a 257 Weatherby put on it. My questions are:
Will this work?
Can I just do the barrel swap from 300WM to 257 and have everything(magazine, bolt face,etc) work for it?

 

[TRG300WM]

I have both these cartridges and both have .532 Bolt face. I would say it would work through the mag box as well and if not, it wouldn't take much to make it work.