Yes you can do all of that post-security. IAD has a single centralized security checkpoint, and both the aerotrain and shuttle are post-security. Aerotrain is a small people-mover train system that runs underneath the airport, you'll have to go down escalators to get to the platform area. The walk between C and D and the walk between A and B is doable, and the train is likely a quicker option, though there's some extra walking to get up and down to and from the platform.

If I recall correctly, the shuttle is in one of the old-fashioned mobile lounges and goes along the tarmac which I think is a fun experience if you haven't tried it before and if it's running! These leave from the gate area, so you won't have to go down several levels of escalators in order to board.

(Last time I was at IAD was early 2016 so my train information is up to date; haven't been in Terminal D in about 4 years, so not sure how up to date my shuttle info is).