This is not rocket surgery.
Place stock in work holding device, chuck, collet or between centers. Place tool in holder and knurl.
If cross pattern knurling run the tool into the work as fast as possible with the required force to make the knurl in one shot, do not be shy here.
A cross pattern requires 2 tools so a scissor type holder makes much sense. In 30 years of knurling I have never once considered diameter/knurl pitch to be important, as mentioned above a tapered part should knurl just fine, have never done it but may give it a try this week just for fun.
I have never used a cut knurl but we do have one so may try that as well.