.dwg version is also available on GitHub
But to directly answer your question, yes, basically change all references from dxf to dwg.
I was able to associate DXF and DWG to Solid Edge Draft with this utility:
(you can create a new extension like dxf and choose "Solid Edge Draft" association for it)
Is there a solution to this issue that does not involve having to modifying the registery?
See the post from @FredMenage directly above your question.