Igorrock is quite correct and you have obviously decided you need a scope. As to 'doing harm' to a particular rifle, anything you do is going to change that rifle for good but a rifle is a tool and it needs to suit both the job and you. Any changes such as mounting a scope should be practical and done to make the best use of the tool. High mounted scopes turn me cold and IMO are not best practice and do not make best use of the tool.

I was faced with a similar dilemma with my original Type A Oberndorf Mauser sporter when wanting a better aiming system than the open safari sights but not wanting to alter the bolt handle or flag safety, the latter being one of the safest in the business, and also not wanting to compromise the charging of the magazine with this 404 DG rifle. I opted for a single point dot sight mounted extremely low in a semi scout position, later replaced with a Leupold 2x EER scope on the same base. The open safari sights are still usable with the scope removed as the single piece Weaver bridge base I used is deeply U'd and does not hinder the use of the open sights.

Although EER scopes are a compromise, they do work well for fast close work and also extended range shooting and provide a good sighting platform as eyesight deteriorates through age or disease. There is now a range of these scopes available in different powers and even a vari-power. The same mount system allows the interchangeable use of a good selection of reflex sights if you ever wished to go down this line.
The semi-scout mount position is perfect for allowing unobstructed charging of the magazine with big cartridges.

No matter what scope mount you use you will have to drill and tap some holes. On your Brno using a reflex sight or EER scope I see it would be possible to install a base as I have on my Mauser bridging the gap between the receiver ring and the rear sight. I used a single tapped screw hole in the rear of my safari sight and drilled and tapped two screw holes on my receiver ring. In your case with the lighter recoiling rifle I would just glue the rear of the bridge mount to the receiver ring using the super strong Araldite epoxy glue available now. The stippling will ensure a good key for the glue which can still be easily removed at a later date if required without damaging the stippling and Brno logo ( a bit of heat and a brush will remove the glue from the stippling and logo on the receiver ring).

A small hole in the rear sight would not be noticeable and could become a locking screw for the dovetailed sight.