I actually just did this just yesterday. I have no idea how my cowl will hold up but here's what I did...
My car is at the shop being painted. Since I had the cowl area and fender boxes down to bare metal already I needed to get in the cowl to keep it from rusting further. There's only light surface rust here and there (the vents and the area under the vents had been sand blasted), but doesn't appear to have any rust holes and looks nice overall.
So I put a small hose in the vent area, attached a funnel to it and poured some POR-15 in there, in a few different places. Then I used a 2 foot metal extension with the little fingers on one end to hold a chunk of firm sponge. (I had to throw it away afterwards but it was $3.) I put it in the cowl access holes on both sides as well as in the drain holes below and wiped the POR-15 all over. I used the shop air to blow the POR-15 in the cracks and crevices since it's tough to manuever with the sponge.
I plan to spray some wax in the cowl after the car is epoxy primed and painted this month. A hint would be to use the POR-15 sparingly; it really goes a long way for this job. Also a bright light or two for peering inside is mandatory.
The best you can do is, assuming you have access to the drain holes is to attach a flexible hose to the end of your compressor and blast all chunks loose and out the opposite drain holes.
What I just finished doing was to obtain a undercoating sprayer with a flexible wand which is 36" long. Got some ZeroRust paint by quart. Thinned it 1:1 with acetone. Covered the grills of the cowl with plastic and stuck the wand in one drain hole and sprayed the heck out of the cowl. Then went over to the over drain hole and did the same.
Without opening up the cowl, you are very limited to what you can do in this area.
How about this idea, on my Toyota truck engine compartment (1986), I remember having to try and spray an area with paint that I couldn't reach, so I got out a WD40 can and switched the spray nozzle with my spray can, then I attached the red "straw" tube to it, stuck it in a hole and sprayed my paint! It actually worked real nicely, and atomized the paint fairly well. If you do this, let us know how it works in the Cowl of a Mustang!