It matters not if a male is neutered or not -- whether he squats or lifts a leg is pretty much a matter of personal preference and how he was 'taught' or became accustomed to it early on. I have a male who does both -- whatever is most convenient at the time.
Those little Glad containers can work well and are disposable. If the dog really is too short-legged to accomplish it -- you can take a wooden yardstick and literally tape (duct tape or whatever works) the shallow container to the end of the yardstick. Then you don't have to bend over (and telegraph your intent for a skittish dog) to just slide it under the side (for a male who squats you really have to get the dish pretty far under them to catch the stream).
DPU *smile* you think like an engineer who knows dogs LOL -- I'm outa luck here tho -- no hills in Floor-daaaaa!!! But now I have my daily giggle -- so THAT's why they hunt all over creation for a spot -- not just smell but ... the right slope??