The Corkscrew is going to add quite a bit of bulk no doubt. Its not really a bulge enhancer in that sense but rather a more serious PE tool for lengthening the penis.
The only way to deal with it is the style and combination of clothing. I personally like wear the Corkscrew down the leg thru the underwear opening. The profile is slimmer this way rather than compacting the mass in any way for a bigger bulge. As I am looking for maximum stretch I don’t want to limit the extension as well.
I wear jeans and untucked button down shirt to fully conceal so I don’t have any problems whatsoever in that regard.
Best to experiment with different clothing combinations and drape with long shirts if you want full coverage.