If you want to go very period correct, you could get the Williams Quick Convertable side mount. Many savage 99s were drilled and tapped over the years for this mount. Let's you use both irons and scope.
I found one on ebay for my 1906ish Savage 1899 in 303 savage. Was something like 35 bucks plus shipping. Williams still stocks the scope rings. Also, I see that they are available on midway.
My experience with it is that it is an excellent mount and rings. I have never had any zero issues and I have made up some kicking loads. I do not use the "quick disconnect" feature, so I cannot verify if it will return to zero after removing and remounting the rings. I bought mine solely for load development.
Here is a pic of a savage 99 mount. If you already have holes drilled and tapped, look for 4 in a row as shown in the pic. I only discovered this mount because I was trying to figure out what my rifle had been drilled and tapped for. I didn't want to make new holes.
you can get rings that stay to the side so you can use the iron sights as well, or rings that are over the bore for scope only use with the benefit of it being centered, or you can get high over bore rings that allow both irons and over the bore centering.
Here is a pic of a rifle with the mount. This isn't my rifle, but it gives you a bit of an idea. If you are interested in finding this type of mount, I can take closer pictures of my actual rifle when I get home tonight. Just let me know.