About the only needed specific kernel compiling, is drivers for specific hardware, that does not already have the driver, in the kernel.
Usually that is WIFI hardware and Graphics hardware manufactures driver. (kernel has the generic graphics driver)
The WIFI hardware is too new for the kernel being used. So, compiling needed driver is required.
But usually the newer kernel has been updated to have the needed driver for WIFI.
The graphics hardware will run with the generic driver that all Puppy versions have.
To get the more featured manufactures driver. Yes it does need to be compiled for the specific kernel.
But that is any kernel you use and any Puppy version.
So far for me.
Changing to a newer kernel has not broken anything that did work before the change.
Changing to an older kernel has broken stuff.
I said try changing the kernel.
change_kernels will make a backup of the old kernel and allow you to change back if you need to.