Craig
If you are happy with your pre-testing and sure that the rug is 100% silk and NOT Art Silk, then it may be OK to clean with your upholstery tool.
Backdust, surface vac, repeat until no more soil recovery is apparent.
Woolsafe pre-spray, agitate gently by hand with pile brush in direction of pile. Dwell as appropriate.
Rinse/extract Woolsafe with upholstery tool, several extra dry strokes all in the pile direction.
Towel dry in the direction of the pile.
Towel dry in the direction of the pile.
Towel dry in the direction of the pile.
Towel dry in the direction of the pile.
Towel dry in the direction of the pile.
Repeat as required.
Groom with velvet/boffin brush.
Groom with velvet/boffin brush.
Groom with velvet/boffin brush.
Groom with velvet/boffin brush.
Repeat as required.
Turbo dry
Silk rugs can be very demanding in terms of both technique and time. Don't cut corners and grooming should be perfect upon completion otherwise pile distortion will look awful.
I wont even go into saturation or submersion cleaning for you.
If you have any doubts, walk or pass on to a rug cleaning specialist.
Safe and happy cleaning
The Ken