My opinion, for what it's worth (of the ones you said you have not done and you only mention the Cascade volcanoes, nothing non-volcanic in the North Cascades so just sticking with the stratos):
Adams-yeah, easily doable late summer without gear but I would recommend taking at least Yaktrax or Microspikes in case the slope between Lunch Counter and Pikers Peak is icy. Would recommend you take an axe and crampons if you know how to use them but likely not needed that time of year.
St. Helens-sure, dusty hike after the melt
Three Fingered Jack-technical rock after the melt on par with Washington that you said you've done.
North Sister- I consider this to be the hardest volcano by the easiest route (did it when snow-covered though) but if you go late summer and are comfortable on a loose, crappy traverse with a fall meaning likely death and a 4th class scramble on crappy, falling, loose junk, it would be "possible" to do it without alpine gear. I think most people who do it do it this way but if there is snow, you will need crampons, axe, pickets, maybe screws/chocks, etc. Please don't let us read about you falling there though. You do have a glacier crossing to get to the ridge though. It's easy on the Collier and the crevasses are usually easily avoided (same route if you did Middle Sister that way, you just fork left off the glacier).
McLoughlin-great hike once the melt occurs
Shasta-Honestly, I would not recommend doing this without axe or crampons because you don't know what you'll run into but I was able to do it without either late season and only used my axe on the glissade. I don't think I'd recommend doing this without either, just saying I hit conditions where they were not needed one time. But I would not do it without having those pieces of gear along.
(anyone let me know if you disagree with any of this, just going off the top of my head)
Oh! And Hood, no, don't do it without the gear and skill to use them, on any route.