The way I understand it, it's not possible to just change Trainer ID/Secret ID and maintain shininess, unless you luck out (basically on the order of rolling "another" shiny). However, depending on where you draw the line for it being the "same" Beldum from an emotional attachment point of view, we may still have some options - by changing the PID we may be able to change Beldum's trainer IDs while keeping its shininess, IVs and Nature (and we can certainly do so if the IVs are allowed to drift a bit).
Here's what you do:
Grab your new trainer ID and secret ID, and make note of the IVs and Nature of your Pokémon.
Download the PID <--> IV generator and run it.
When you get to the menu, choose option #3 and enter in all the data you wish to keep - the IVs, nature, and Trainer ID numbers. If it spits out a PID, you're done - there's a match for your new identity, and you can plug the given PID into Pokesav.
If Step 3 didn't work, try menu option #2, and enter IVs slightly lower than the ones you recorded - it'll give you a list of possible PIDs and IV spreads to choose from.
If you don't want to go through this, or if you couldn't find a good match to your original Beldum, there's one other possible solution: using Pokesav to change your own trainer ID and Secret ID to match your Diamond game. If you want to go this route, you can use Pokesav's "PID/IV" button to migrate your already-caught HG team over to the new trainer ID - they won't be shiny, but they probably weren't shiny to begin with, so it should be OK.