Need a good Yubikake

Does anyone have a recommendation for a really really good Yubikake? The fabric of the knitted ones are irritating my skin.

All Japanese yubikake are made of a very similar kind of material.
Your best bet is to make your own, crocheted out of silk thread (which is naturally hypoallergenic).
Ideally, you would use silk thread with a few percent of some elastomer (stretchy thread), but test for irritation first, as elastomers may cause you skin irritation as well.
I guess you can possibly contact a Japanese store, and ask them if they would know a manufacturer that could make a custom silk one for you.

By knitted, do you mean:

image

Those make me itchy too. At least now that it’s gotten very shabby.

However:

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If sized properly never does.