BE20 pilot reported loss of brakes while parking; resulted in loss of control and contact with a C172.

Narrative

Brakes were operational upon departure. On final approach to XX at the ZZZ airport I checked the brakes and discovered the brakes felt very soft on pressure. I landed without incident; informed tower and ground that I had no brakes. They asked if I needed assistance and I said no; but I will taxi very slowly using reverse thrust. I taxied without problem to the parking area at the ramp. As I maneuvered to park I felt a little pressure on the brakes and thought I might be getting some braking action back. I came to a stop using reverse thrust and pushing on the brakes taking care to park far enough away from other parked aircraft (3 parked planes in front of me on the next line up). Nobody came out to marshal me in or park me and I didn't see anybody else on the ramp. I proceeded to shut down the right engine and as the propeller changed pitch on shutdown and started to move into feather; it made the airplane accelerate forward. I had no brakes at that time as the aircraft rolled forward and started turning right due to the left engine still running; but in beta flat propeller pitch (maybe some residual thrust). I quickly ran out of room and time as the airplane rolled. I feathered the left prop and kept mashing on the brakes and right rudder trying to keep the airplane turning at that point. In a pretty slow turn with no brakes and engines spooling down from shut off; my plane came into contact with the middle plane parked on the front row. My left propeller (feathered) but still turning hit the left horizontal; left elevator and rudder of the other plane causing damage to that airplane and two of my left propeller blades. The aircraft came to a stop at that point. Nobody was in the other parked plane that was hit. Nobody was hurt or injured.Looking back on it; I would have called on the radio to have someone come chock the plane from behind the wing before engine shutdown. However; it's still not the best idea to introduce other people into the scenario where I don't have full control of the movement of the airplane due to no brakes. Shutting the engines down on the taxi way was questionable as well due to possibly rolling off the taxi way into the grass towards a drainage ditch that could have been there. Getting the airplane chocked is probably the best idea; but I don't like the idea of bringing other people around a running airplane with no brakes.