You really don’t want them eating fabric. The HRS recommends a cotton towel since the fibres (cotton fibres) are short and won’t do major damage if accidentally ingested. But it is also recommended to remove the towel if they are eating it. I definitely would avoid any artificial fibres (and I strongly suspect something “silky” is likely to be artificial) since you are likely to have long threads that could be dangerous if ingested.
I suppose it can be said if you pick up fibres that have been torn they probably aren’t eating it, … I’m too cautious for that, if it has holes in it then they don’t need it that badly is my thinking. I’d rather have a towel deprived healthy rabbit then the opposite.
Some people have been able to give their rabbits artificial fleece (short fibres again) testing them first to see the fleece doesn’t shed easily.
There are lots of toys that are fun to push around, and a grass, sea grass or straw mat are all good worry free choices for them to lie on. And they can surprise you, … mine can’t be near a towel without eating it, but their two sea grass mats are favourite spots to stretch out on and were only nibbled in passing the first week or so and have remained untouched for three months.