We've also stayed in a BWV handicap 1-Br. The whirlpool/vanity part of the bathroom is the same as you are used to, so don't worry. It is the part of the bathroom that also connects to the living room that is different. This is the part with the commode, pedestal sink and shower.
We really prefer the shower set-up in the handicap units. The shower is larger and the large bench folds up against the wall when not needed.
We were also told that the bathroom in the 2nd br./studio is also handicap accessible - as the entire until is accessible. Now what that means to Disney, I'm not sure. At BC my DB (requires a stall shower with a bench) had an 'accessible' room with a tub.
Anyway, you 'may' have some flexibility as to which bedroom/bathroom you give to your parents.
I just noticed you mentioned a standard view. ALL handicap villas are preferred view. There aren't any with a standard view. When BWV was built, there weren't any standard or preferred views, so it wasn't a concern.
You should ask MS about the possibility of getting a portable seat for the shower - but that will be pretty tight spacewise. It would be better in the 2nd bedroom tub - if she can get in a tub.
As to location if you decide to go for a preferred view, all the times my DB has stayed at BWV, they have had the units that are just around the corner from the elevators overlooking the main pool. He has been very impressed with how quiet the bedroom is, considering the head of the bed is against the elevator shaft. They have never heard ANY noise from the shaft. (He once had an office next to an elevator and HATED the noise all day long.)