Been using the cut off wheel on a Dremel too. The only difference is that I keep a cable that doesn't have an end on it for brake or shifter and run it down the housing to knock out the lining hole. This approach cleans it from the inside out rather than pushing anything into the lining when using an awl or other tool from outside the lining.
not all cable can be soldered so i use super glue for about 1/2" along the cable. Also avoids using an end cap.

I get a perfectly clean cut on cables with a Felco cutter. On housing, it bends the end of the coil slightly so that parts needs a little filing.

https://www.felco.com/us_en/our-prod.../felco-c7.html

Having used most Pro cutters such as Park, Shimano and Pedro's at the shop I work at none work as good as these https://www.amazon.com/Apex-Tool-Gro.../dp/B000TDDP6E ,Crescent 8" Pro Series Diagonal Compound Action Dual Material Cutting Pliers - PS5429C. I bought my first pair at lowes and fell in love with how easy they cut, so I used them for everything then I bought another pair and use that pair for Bike only cables, my old pair is used to cut old cables off bikes and even cut a spoke or two ( Don't recommend them for that ) . These work great for SIS housing as well as any other housing or cable. Even my boss got a set for the shop after I bought mine in to show him how well they cut and how easy they cut.

Glenn

I have been using Park tool for months now, and I love its consistency. This product is one of the small cable cutters that leave clean-cut marks. This cutter can trim brake housing and hard-to-cut shift housing on your bicycles. It has heat-treated and cold-forged handles, which are strong enough to snap bicycle wires.