Fletcher is a much better brand to get, I recommend the carbide tipped ones vs the steel ones. https://smile.amazon.com/Fletcher-Pattern-Cutting-Stained-Carbide/dp/B001G0TKU4?th=1

Otherwise if you want another style handle, the "Top Tools" cutter from here or any other site that may have it is a good option. https://www.anythinginstainedglass.com/tools/glasscutters.html

I use the top tool cutter for class and personally quite often so I can vouch that they will work fine once you know how to hold the handle type correctly.

As for oil, ignore it, You don't need it. It's only there to protect the shaft inside the cutter from seizing over time.