I make my own mirrors and telescopes.
The method recommended by Gary Seronik, that you linked above, is very good, and it's widely used. A few comments:
Don't be afraid to touch the mirror with clean paper. The vast majority of mirrors these days are over-coated with SiO(x) and are quite sturdy. Maybe wash the mirror before you do anything else, this way you'll remove potentially abrasive dust particles. This is how: https://www.youtube.com/watch?v=9Y8xFnXFVGQ - it's a good idea to wash the mirror anyway, like once a year or every other year.
When making the big paper template, cut the disk from a piece of paper without wrinkles. Draw a good circle, and cut it carefully. Make sure it's flat and it doesn't want to roll up. When centering it, go over the edge again and again, and adjust it so that it's perfectly centered. You center it by working out the edge alignment with the mirror. Take all the time you need.
You could also cut the template out of transparent plastic, larger than the mirror, and just draw a circle on it, the same size like the mirror. This method is recommended by Jim Fly (of Catseye) even for quite large mirrors.
Both versions (paper or plastic) work about the same IMO.
It may take a bit of trial and error to put the central dot on the mirror without smearing it. The marker tends to smear up underneath the paper. Practice on a random piece of glass or polished metal.
The reason why Bob Fies (of Alcoat) says it's not for lasers is that, the way he shows it, the paper dot is solid. Of course it wouldn't work with a bare laser - you need a donut shape, with a hollow center, to allow the laser to reflect (when using a bare laser, not with a tuBlug). Just use a little donut instead of a solid paper dot, for the final step - like Gary shows on his website.
If you never use a bare laser to adjust the primary, a solid dot is fine. But a donut gives you more options.
I've done business with Bob directly, he's very experienced. Like Gary Seronik and Jim Fly, he should be considered an expert in this field. But take his advice in context and look at all the details - he says what he says for a good reason.
The way to gauge the existing donut is also by using Gary's method. Make a paper disk with a hole in the middle, center it on the mirror, and put a little dot with a marker on the glass. Compare that dot with your existing donut.
Wipe the marker dot off with alcohol and a q-tip when you're done. You can't damage the mirror unless you press very hard. The center is shadowed by the secondary mirror anyway, so it doesn't matter.
Do everything very slowly and be as precise as humanly possible. The precision of the central donut is critical for the precision of your collimation. Since you only put the donut on once, it makes sense to do a very slow but very high quality job.
If the existing donut is off-center even a little bit, don't hesitate to remove it. If alcohol soaking doesn't remove it, try acetone. You may have to clean the center afterwards, but that's okay.
After everything is finished, clean the inside of the donut with alcohol and a q-tip. You need that surface relatively clean, for the laser to reflect back into your collimator when not using the tuBlug (just bare laser). It doesn't have to be squeaky clean, just remove the marker smears, more or less, and make it nice and tidy.
Congratulations on taking the right steps. Many, many people don't care about collimation, and it's so important for overall performance. Keep that scope collimated.
The tuBlug is an excellent tool for collimation, it makes the process a snap. Great choice. Catseye is another great collimator, but if you have the tuBlug and a Glatter laser (one of the most precise lasers out there, BTW) you probably don't need anything else, unless you have some extremely low f/ratio on your scope (not your case).
I use the tuBlug every time I do an observation. It's taking maybe 2 minutes to do the adjustments. Totally worth it.