Sure, it can be done...
But consider the cost/benefit.
#1)The .25-06 is already over bore, with all but the the slowest powders. The .257 Wby is even worse in the respect.
#2) Weatherby barrels are freebored, and normally 26". This plus the large case capacity is what gives them their velocity advantage. You could convert your .25-06, spend the time and money, and wind up with a rifle that might not even have a 100fps velocity advantage over what you started with.
#3) The converted rifle might not shoot as accurately as what you have right now. The work is going to change the harmonics of the gun, and while you may be able to find a load that shoots as well, or better than what you have now, there is no guarantee.
So, the cons are cost, potential change (loss) of accuracy, and minimal velocity gain (possible).
On the other hand, things might go just right and you could wind up with an accurate rifle with a significant (meaning usable) velocity increase. Its a roll of the dice which way, and how far things will go. Your gun, your money, your choice.
Myself, I would just buy a rifle already made in the Wby round, but that's just me.
All else being equal (and it almost never is) bigger bullets tend to work better.