In the past I have used Shellac as a prelude to wax finishes but I am worried about how it might react with a final finish of varnish or lacquer (ie not wax or oil).
There should be no problem there if you do want to stick with shellac.
Generally speaking shellac will work under just about anything, it's actually widely regarded for its nearly unlimited compatibility.
Focussing on cellulose SS, I am guessing that it works like shellac but it is cellulose that is deposited in the wood instead of Lac-bug resins. This sounds fine given what wood is made of (and my experience of hardening tissue paper with cellulose thinners as a young lad making model aeroplanes). Is this correct?
'Cellulose' sanding sealer should be a dilute form of nitrocellulose lacquer so actually only shares some underlying chemistry with wood.
Regardless of whether the chemistry were similar or not it's not something you need to concern yourself with. Many of the best products used in woodworking are completely unrelated, but yet they work brilliantly with wood — this includes PVA glues, polyurethanes and epoxies of different types, linseed oil and shellac.
I've been led to believe that standard shellac is good under wax or oil based finishes but, if you want to use a varnish or lacquer then you are best using de-waxed shellac.
The basic idea here seems to make sense but it isn't as simple as some people make out, i.e. that the wax will cause a bonding issue. Prior to dewaxed shellac even being available other finishes were widely used under and on top of it, indicating both that it sticks to them and they stick to it.
Certain specifics are going to play some part here, e.g. the wood species, if it was sanded how finely it was sanded, how much shellac was actually built up before the other finish goes on and of course what the other finish is. But there's clear evidence that you don't have to religiously use dewaxed shellac to ensure compatibility with other finishes, in particular a light coat applied in the normal way you'd use sanding sealer can be virtually guaranteed not to cause any problems with anything.
One further option
Sizing the wood is an alternative that you might like to experiment with and consider using in future.
Size (dilute glue) can work really well to reduce or eliminate blotching and was the traditional way this was dealt with. Thinned animal glue (hide glue, Scotch glue) was what was used traditionally as you might expect but today some use diluted PVA glues for the same purpose and report good results.