Can a S&W 625 handle the .45 Magnum?
Probably not.
It may be able to handle the .460 Rowland though. The .460 Rowland is "juicer" than the .45 Win Mag.
From Hodgdon's website:
.45 Win Mag
230 GR. HDY FMJ FP
COL: 1.555"
H4227 25.0 1259 29,400 CUP
H110 28.0 1410 29,000 CUP
HS-6 17.0 1296 36,600 CUP
HP-38 10.8 1191 37,100 CUP
.460 Rowland
230 GR. HDY XTP(Maximum Loads)
DIA. .451
COL: 1.270"
LONGSHOT 12.0 1336 39,200 CUP
Clark -
http://www.clarkcustomguns.com/revserv.htm#rowland
will convert a 625 to .460 Rowland for $99.00
You can call them @ 888 458 4126 if you're serious about wanting a more powerful round and don't mind all the extra cost/effort.
It is cheaper though than it would be to pick up a model 29 or 629 in .44 Rem Mag. - which the .460 Rowland pretty much equals.