Side mounts can be and have been done on the Mosin Nagants, but not by me. All I can tell you is that it's been done. I would go for the side mount before I ever went beck down the road of the "no gunsmithing' mounts that replace the rear sight. They just don't hold up to the recoil. Even for short money, you won't be happy. Replacing the original rear sight with a large aperture ring may be a good sight picture, otherwise you could mount a peep on the receiver.
I spent some time and money putting scopes on a '38 Mosin and some other military rifles over the years. I have decided that the money spent trying to turn an old military gun into a budget hunting rifle ends up costing more that a budget hunting rifle. Mossberg and Savage both have reasonably priced bolt actions. They may not be family heirloom quality weapons, but neither is a sporterised WWII relic. There is also the Handi rifle for short money.
Not trying to talk you out of doing whatever you want, just sharing my lesson that I paid full price for.