I don't have any special cart for older records. All of my vinyl is 33 1/3 or 45RPM long players. I don't own any 78s, though I thought about building a small collection of Duke Ellington 78s until I saw the prices they fetch, and then I was cured of that idea forever.
I do have a lot of mono LPs, particularly from the 1950s.
This is the real deal, issued in 1957. I am listening to it right now on my Ortofon Jubilee cartridge and it is pure heaven. It was later issued as an RCA Living Stereo title (which I have as well). But I actually prefer many of what RCA dubbed "New Orthophonic High Fidelity" recordings which were all mono.
These LPs, if you can get them in great condition, sound as sweet as anything else that has been played on my turntable. I was fortunate enough to be in the right place at the right time, and I bought a box of 80 original RCA Victor Orthophonic LPs that were in minty condition for $100. The buy was easily worth several times that much. I put them in my car as quickly as I could and drove off before the seller could change his mind.
I think you will be fine using your Shelter with old mono records so long as the vinyl is in nice shape.