View this topic for the correct procedure to update everything in Slackware, including kernels. Learn from my hard experience.
https://www.linuxquestions.org/quest...kg-4175663318/
I would recommend that you add the kernels to the blacklist by removing the #(/etc/slackpkg/blacklist) - update everything else in Slackware and reboot first. Then remove the kernels from the blacklist (rem it out) and update the kernels.
People advise to install the new kernels alongside the old kernels and I would recommend this as best practice. However, I am of the opinion that a kernel update breaking your system is very unlikely - the only problem you are likely to encounter with updating the kernels is not doing it correctly as seen in my topic. So I am not too worried about that.