If it's an "Fn+F#" combo, perhaps, but IME many laptops with absolutely dedicated "Media Keys", which may or may not include one labelled for WiFi on/offability have a service or other background process dealing with such extra-clavical buttons.
May or may not be relevant to OP's model, of course. Check to see if there's a configuration utility. Intended to change what program the envelope/email button opens up (if that applies) It could be that you can set it to "do nothing" as well. If not, you might be able to at least find that by disabling the MediaButtons service (whatever it might be called) from starting up (however it does) the whole lot become moot.
OTOH, there are some manufacturers who do tie it much more firmly into the hardware. There should still
be a configuration utility (unless it gets tied into "Whatever program opens .eml files" through the device driver (<-which might be worth looking at disabling altogether, if that exists) and whatever method it uses to push the OS into opening the required programs) and this should still have a "do nothing" option.
Or, perhaps what I should have done is said that while I don't really remember how HP Pavilion machines are set up, I could search and see... Well, looks like most people are complaining when they
don't work, but perhaps those pages have a "this is currently turned off/disabled, re-install it" that can be reversed to "this is what you need to turn off/disable, or uninstall". To get that, try "HP Pavilion media keys", or some variant thereof, via your favourite search engine. (Model number might be useful to tie it down.) Although it's possible that this might bring up on-screen "media key" things as well. I'm not
entirely sure that's the correct term, but it's what
I use when I try to convey what I think
you mean.