I can't speak directly to shooting 32 cal Buffalo Bore, but I have shot BB in other calibers and they are noted for their extra punch. You should check with Buffalo Bore to see if they recommend shooting their ammo in a 60 year old gun.
I have no experience with BB ammo in .32 and in Walthers either.
But BB is usually quite specific in publishing any recommendations if they think their loads should only be used in certain guns. And most .32 pistols out there are older and some are less robust than the Walther.
Since I assume you are contemplating the BB ammo for “serious” purposes only, not to run boatloads through the gun just plinking, I wouldn’t overthink this.
I sometimes carry the walther concealed for self defense purposes. I reload for it and have 400+ 71 grain full metal jacket bullets to mainly plink with. The buffalo bores would be used to stop a man/critter.