No experience of silk wall panels Doug, but have done the usual dry cleaning of curtains and some upholstery and also wet cleaned upholstery.
The inspection will be crucial though. As you and I both know, but perhaps some less experienced may not be aware, silk is prone to not only sun fading, but also sun rot. A rotted area may look intact, but the lightest of touches can break the fibres and ruin the fabric. This can happen generally or may be restricted to just one particular colour.
If the panels are cushioned behind, you'll need to know what the fillers are as these could bleed through.
I wouldn't advise using your truckmount wand though. not even with a glide fitted

If is passed all the thorough tests, I would be tempted to a Woolsafe dfc or microsplitter and towel, or perhaps in severe cases a CFR upholstery tool type of rinse with an 01 jet.
Safe and happy cleaning

Ken