Couple important things:
1) Find the path in. I have not taken my truck's cowl off, but on our Jeep and a Land Rover I have, if you remove the plastic cowl cover there is an open hole pretty large where any rodents can just walk right in (unless you have the cabin filter). They can get down into the top of the blower. If they build a nest in there, it's ok ....until the moment you go to turn on the fan ..and blow bits of nest all over the inside. You don't want it to clog your HVAC system drain hole or else water will run all over your carpets ..and could lead to floor rot. What I did on our land rover after dealing with the same thing as you, was make a fine wire-mesh screen over the hole ..about a little less than 1/4" mesh. So far so good.
2) You need to suck out the pieces: This can be a *****. Use your shop vac and may even need a piece of small flexible hose that you can stick in further. Beware if there is any sensors or thermal switches inside because you could easily break them and that could cost $100. So, remove them if you see any. I had to use a bore scope in mine to get all the little pieces out of my Land Rover's fan area up to the evaporator core.
3) Mouse Pee really stinks! There's something about mouse **** that is particularly pugnant. Normal disinfectant isn't going to cut it, it'll return. However ...I know a secret formula (sort of), Actually I don't remember the formula exactly but there was an episode of Mythbusters that dealt with this topic. None of the supposed anti-mouse formulas worked and they came up with a formula out of household products that actually works ..and better than expensive commercial products. I used it on my Land Rover (which by the way was SO bad inside I couldn't stand to drive it, even in the cold winter). So go to youtube and search for Mythbusters mouse pee (or *****). It's something like: Water, vinegar, soap and baking soda. I mixed up a batch and put it in a bucket, then used a small fountain submersible pump and fed a hose into the hvac area (with a nozzle I made) and hosed it down. Make sure the drain is unobstructed ..and suck out any wet remaining bits. That was about 5 years ago and to this day you CANNOT smell even a hint of mouse pee! It actually smells kind of nice and fresh actually.
Good luck.