Is it okay to put an instant hot water dispenser on the garbage disposal wiring?
The main rules that I am aware of (but I am not a professional electrician) are:

Total planned usage should be &lt; 100% of total and &lt; 80% continuous usage

With a 20A circuit, 80% = 16A. 15.75A &lt; 16A, so you're good there. Actually, the disposal would likely not count as continuous anyway, but since the numbers work, no problem.

If hardwired loads are &gt; 50% of the capacity of the circuit, then you should not have any receptacles for plug-in loads.

This is where you could get to a problem. 9.5A is under 50% of the total, but more than 50% if rated at 80% for a continuous load. I don't think that is a problem. It is certainly not a problem if you either have both loads hardwired or both using receptacles. However, the instant hot manual only shows plug-in and the disposal only shows hardwired. Unless there are alternatives officially supported by the manufacturer, you should not be switching things around - i.e., don't change the disposal to plug-in or the instant-hot to hardwired. The switch you linked is specifically for use with a receptacle.
My recommendation:

If power goes from circuit breaker to disposal to switch, then you already have power in the right place.

If power goes from circuit breaker to switch to disposal, you will need to run an additional cable between the switch and the disposal and move things around a bit. But unlike many other situations, this should be pretty easy since it is all near the sink and should be easily accessible. We can outline all the specific details if needed.

Below the sink, you will have a box with:

Power coming from the circuit breaker
Switch loop going up to the switch
Disposal connected to the switch loop
A single receptacle for the instant hot