Does the balalaika have a maker's name or anything on it to identify it? If so, then try and check with the maker. You could try measuring the original strings with a micrometer (or similar) and then if you know the tuning for the instrument you could calculate the overall tension using one of the above calculators. Select your strings so that the overall tension is still the same and that the tension per string is about the same (to ensure an even balance across the bridge) and you will probably be OK. That's what I did for my bouzouki but I was also able to consult the maker (Fylde) to see if my choice was safe - you may not have that option. What ever you do, take it slowly, check the neck and bridge (if it is fixed) for signs of distress and back off immediately if there is any hint of trouble.