Accord shake in rear when braking

Lately my '93 Accord with 217,000km (~ 135,000 miles) has been exhibiting
a minor shake in the rear when I brake. It feels like it is moving
slightly left and right, but not in a rapid motion. And it tends to be
more pronounced when I go over a bump while braking. When accelerating or
cruising, the shake is not there; it feels normal.

The car got new tires and a 4-wheel alignment done 5000km (~ 3100 miles)
ago, and the tire pressures are currently at 30psi all around (Honda
specifies 29psi). I was thinking that the problem could be with one or
both rear brakes (these are drums), or with the rear shocks. The shocks
are not the originals; they are aftermarket Monroe's that were on the car
when I bought it 5 years ago.

Am I correct in my (non-expert) thinking? Any other suggestions? Thanks
in advance.