If it works better for you, it is absolutely fine to do so. I myself do like the technic Tom Spellman showed in the video. You don’t have to slit the blade under the bark. You just make the first cut down onto the hardwood and then twist the knive. This does the job for me very reliably plus it doesn’t hurt the bark to much since with that twisting motion the blade lifts up the bark a little and dosn’t just push it aside.
But actually the trick is to do a bark graft at the right time. The tree has to have broken dormancy. Only when it already pulls sap the bark will slip. If you hit this condition you shouldn’t have problems lifting the bark. When I realise the bark doesn’t slip properly I then wait some days to do a bark graft or simply change technic. E.g. you then could do a side graft or another one we call “Geißfusspropfen” as shown in this video. Both those technics don’t require the bark to slip.
I should mention it isn’t necessary to use such a heavy blade and a hammer with thinner limbs. But of course that technic is much more challenging than a bark graft. I rarely use it and don’t feel comfortable yet doing it cause I’m not very good at it.
Here it is shown (it’s in german but I refer to the picture). Dammit there was a really good video on youtube about this technic but it is no longer available.
http://www.mein-garten-ratgeber.de/veredelung-methoden-details/kopulation.html#geissfuss
Works very well if done right