That hub has a freewheel, not a casstte. You need the right tool to fit the splines or notches on the inner part of it. Depending on what kind of freewheel it is, it may be hard to find the tool, but a bike shop should be able to get it off. the last resort is to disassemble the freewheel on th ehub, then use a pipewrench to remove the inner part of the body.
Once you get the freewheel off, put a track cog on it with an old style bottom bracket lock ring, respace the wheel for the correct chainline, and you're good to go. Keep the brakes.