Some latigo is pretty hard - the mexican stuff feels like it is some sort of board when you cut it, and draw gauges and plough guages wander and even head, half round or french half round knives need more than one pass.
Some latigo on the other hand is very soft and almost any craft knife, stanley knife, head knife, etc will do the cut in one pass.
Paying attention to what is under the leather is important - steel or glass will blunt the knife whereas timber or rubber mat will not. I use a very long self-healing cutting matt, but along with specialist gauges and knives, it is quite expensive, so I suppose timber will be best in this situation.
If you are using a steel edge as a guide, you do not want something that has high sides as the body of the knife will contact it. You do not want something with handles that the knife handle will touch, or any protuberances. A simple steel rule is best, better if you stick some anti-skid to the bottom of it. Clamps can hep if you have an extra long straight edge, but make sure the bottom is cushioned with anti-skid mat and that you do not tighten the cramps too much, else the body of the straight edge will get imprinted in the leather. The cramps should be just out of the range of the knife, else they will get in the way - a soft touch in the middle of the rule is all that is needed then.
It really is a simple matter, like Pixelfixed says - don't over-complicate it and just go for it, as you say the strop gets little or no use anyway.
Regards,
Neil