What permissions/rights are needed to run regsvr32 /s /c "myocx.ocx"

Via regedit you need to give the build account rights on "HKEY_CLASSES_ROOT.

Right-click on HKEY_CLASSES_ROOT and choose Permissions...Full Control.

Registering an OCX comes down to writing entries in the registry under HKLM. Non-admin accounts by default don't have rights there, and I'm not too sure your build account should (installation of debugging OCX's is still "installation" (v.s. building) in my book).