Blue Tac is Cool.
The pics below are different color balances (one flash, one without, then both adjusted.... mainly because I suck at taking pictures).
The second picture shows the second application of Blue Tac. I did so immediately after the first; you can see there was still some grime to come up.
It's harder to do the inside threads of the body, but I used something like the front-body of a ball-point pen to press the Tac into the body threads and roll around til it's a full circle.
TIP: The Blue Tac is easier to handle when it is not too warm. Using it makes it warm up (kneeding) and just like silly putty has a "best texture" point that you will discover for yourself.
Threads feel smooth and even as if there is a healthy play between the threads as it screws together.
This stuff is great! It's reusable, so one pack will last months if not more.
It looks like DeToxit may be unnecessary, though I have not tried to use it after the Blue Tac as a "test" if there was anything left to clean. Perhaps at one point I may... But this is way easier!