I am new to reloading. How safe would it be to replace factory Weatherby 117gn round nose bullets with another bullet of the same weight using the same factory powder?

It is 257 Weatherby

as long as you don't replace a typical cup and core bullet with a monometal you'll be fine.

But bear in mind that some Weatherbys had a 1-12" twist barrel and won't stabilize the 117 BT spirepoints.

its a 1:10 Vanguard. I am guessing a 115 would not work. Right?

That combination should work just fine.

Are you saying: Pull the original Wby bullet. Use the original Wby powder and replace with a different bullet of the same rate? If so, the length of the new bullet might require that you seat it deeper or manybe not as deep as the original bullets were seated. If the seating depth is different the pressure will be different and, thus, the velocitiy will now be different. Although the pressure probably won't be too high, you'd just have to shoot them to see how accurate they are.

No offence intended, but it seems to me a barmy idea, especially if you plan to don't resize (and prime again) the brass. Pulling the factory bullet will likely alter the neck tension and switching from a bullet to another, even of the same weight, can give unpredictable results....