One of the reasons I focus on Ubuntu-or-debian binary compatible Puppys is that the creators of video-editing applications have those, rather than Slackware, in mind when building. Not that there can't be Slackware versions. It's just that the 'user' can't just be a user. (S)he often has to track down components which the application creator didn't include. For the most part, video-editors are built onto a python frame-work, and resolving python issues is beyond me.
I took a look at both KDEnlive and Openshot for Slackware-current via pkgs.org. The third-party (i.e. not official) build via the links to slackel and slackonly repos seem the least intimidating. I'd guess that the best way to acquire them and their (perhaps unnoted) dependencies would be to install and use pkg-cli.
shot-cut might be the easiest full-fledged video-editor to get up and running under Slackos. They publish just one build for a variety of Linux distros, although Slackware isn't mentioned. And it's available as a portable which, under Puppys, should make it easy to 'trial-and-error', search for what's missing, try-again without messing up your system. https://shotcut.org/download/.
MikeWalsh has published portables of both shotcut and openshot, viewtopic.php?f=88&t=3375. If they don't function OOTB under Slacko, they might provide a good base to build on.
Edit: As I mentioned, I usually stick to 'Ubuntu/debian' Puppys. But mistfire has published a QuickPup64 21.08 BETA 5, viewtopic.php?f=33&t=3171, having builtin so many modern applications and 'Bells & Whistles' that I had to 'check it out'. As it's on my 'boot-menu', your post encouraged me to boot into it and check out the AppImages and portables I've accumulated. MikeWalsh's portable openshot opened OOTB as did his LosslessCut. His shotcut complained that jack was missing and wouldn't open. Avidemux_2.7.6.AppImage opened; 2.7.8_GLIBC_2.28 did not. The KDEnlive-19.04.AppImage also opens as does the Olive (April 2019 | Alpha | 1e3cf53) AppImage build.
Whether any of those applications are "fully functional" under Quickpup, and to what extent they will function under your Puppy is beyond my knowledge. But, hopefully this will provide you with some ideas.