Nanopowders down to 30nm are usual, at least for graphite and MoS2
(as lubricants). Please protect your lungs.
I found quickly the refractive index of silicone oil: 1.402 to 1.404. For transparent rubbers, it must be available too. Pure silica has 1.46 at 550nm, rather good match. Unmodified castor oil has 1.47. Ask an optician if this match is good enough, or experiment with silicone oil and silica.https://refractiveindex.info/https://www.filmetrics.com/refractive-index-database
Fluorosilicates (and very few others) have a smaller index, glasses tend to have a bigger one, TiO2
and similar much bigger.
1m transparency is very difficult! For instance banal glass 0.3m thick is dark green. Silica and fluorosilicates are transparent over 1000km, PMMA is very transparent over 0.4m, for silicone I don't know. This constraint is extremely restrictive.
Several classes of silicone exist, even within the most common dimethylpolysiloxane. It depends on the processing path: prepolymer, solvent, cross-linker. For 1m transparency, every trace of remaining solvent and catalyst matters, so this choice can be made early.
Silicone rubbers have extremely varied stiffness, depending on the cross-linking and on the length of the resin oligomers. You have two adjustment possibilities here, which may be useful, as I suspect that your rheology doesn't boil down to a single parameter.
The silicon glue I used on my satellite was extremely expensive because the manufacturer made special small batches containing no silica powder (and because these customers are rich). I believe it was Dow Corning 93500. One European alternative existed then, even more expensive.
Would a liquid containing much powder resemble your needs? A thin powder won't sediment, as Indian ink shows. I fear the suspension will be brittle before you obtain a flowing force threshold. Little water in glycerol adjusts the viscosity and 0.1 is very transparent. Polyethylene glycol comes in any viscosity.
The paraffins I saw were translucent, not transparent over 1m. Mixing them from pure straight alkanes, you can adjust the melting point or melting range so they creep at your desired temperature. Octadecane melts at +29°C.