I'd definitely stay in the E dock when arriving from HKG, use the F lounge there. You'll have to pass a security check within E dock.

About 1hrs prior to departure (most probably from A gates) go towards "Transfer to A". No security check, you'll ride the Heidi train, then immigration (into the Schengen zone) before entering A terminal.

You could cut it closer, but if you're unfamiliar with ZRH and Europe in general, taking a bit extra time won't hurt. You can also use the F lounge there, and ask how far your gate is from the lounge so you'll not leave too early.

Keep your boarding pass from the F flight to gain access to the F lounges, since you'll be using them as "arriving passenger".