I have seen replacement units. I have never seen replacement parts...if such exists, they would have to be welded.
These shakers contain hydraulic fluid inside..and I am not sure what welding heat will do to the inside.
I would be concerned about heating up a closed unit ..especially to the temperatures that are needed for welding.
I would definitely open the top and drain them, and keep them open while welding.
(They are technically called Ballasts..I assume you have a convertible?)
Vic