For the record:
Your specific question "is it bad to use a slash here?", in my opinion it is bad to use a slash in your specific example, for this reason:
Note that you can in fact perfectly replace the slash with a " or ", in this case.
In my opinion, if that sentence in italics is true, you should do it.
Note that in other situations you can not replace a slash with an " or "; IMO it is then good and proper to use a slash.
Your specific question "Is there perhaps a formal rule about this?" There is no such formal rule. In different "specific style books" they may have a rule. (For example, ScientificAmerican magazine writers may have some specific house rule.)
In my opinion, the logical and good rule to apply is if you can in fact perfectly replace the slash with a " or ", then choose the " or ". But that is just a formulation I have come up with, applying all the broad general thinking on slashes and " or "s. i hope it helps!
Note In my opinion regarding your specific sentence. (This is -extra of your literal question: a long-standing tradition here on ELU!) I believe the best thing to write is simply "click" because that applies perfectly whether there is actually a physical click (eg with a mouse) or when describing a button on a touchscreen. My reasoning for using one word rather than two (regardless of slash/or issues): you are always always better to "K.I.S.S." in writing. if you can cover all relevant situations with one word, do that.
An important point which has arisen: note that regarding virtual controls on screens. We use the entire gamut of words which could refer to real physical controls, on, virtual controls. (So, words like turn, throw, slide, in, out, positions, clickstops, springs, click, push, etc etc etc.) This is normal and utterly established.
Just another minor point" note that the virtual controls on PC/Mac screens, are indeed, just as virtual as the virtual controls on toushscreen devices. It's true that a mouse has a "real" click, but when you say "click such and such button on the screen" you're talking about the virtual button, not the mouse. (Note too that within a short time, all screens everywhere will also include a 30 cent touch layer, so there will be no distinction between with-mouse devices.)