1. Some touch words that were once in common use in English, but are now obsolete:
felth -- the power of feeling in the fingers (and other parts of the skin); like sight and hearing
hardel -- the back of the hand, as "palm" is the other side of the hand
wrine -- a deep line in the face; a "wrinkle" is a shallow wrine
yespen -- a double handful; as much as two hands can hold
feelsome -- a word describing something that is a pleasure to touch; velvet would be feelsome
lithesome -- flexible
handsmooth -- flat and level
to chumble -- to crumble something into tiny bits
to twingle -- to twine around
2. And here are some touch language items that aren't obsolete, but that would usually be found only in medical or technical writing:
knismable -- ticklish
knismogenic -- producing a tickling sensation
anaphia -- lost (or diminished) sense of touch
palpate -- to examine by touching
skinfeel -- a term used by experts on product standards; for example, for hand lotions and shampoos
thigmoreceptor -- receptor cell for external touch
proprioceptor -- receptor cell for internal touch
3. Many sets of English words for sensory experience have words for sight and hearing but no word for touch; some examples follow.
"I didn't just see it by accident -- I was looking."
"I didn't just hear it by accident -- I was listening."
"I didn't just touch it by accident -- I was ....?...."
"I didn't just feel it by accident -- I was ...?..."
"Look at me when I talk to you!"
"Listen to me when I talk to you!"
"....?... ..... me when I talk to you!"
"You're the apple of my eye!"
"You're music to my ears!"
"You're ...?... to my skin!"
"Mary's nearsighted; Ann's vision-impaired; Tom's blind."
"Mary's hard of hearing; Ann's hearing-impaired; Tom's deaf."
"Mary's ....?...; Ann's touch-impaired; Tom's ....?....."
"The image we saw was perfectly clear."
"The sound we heard was perfectly clear."
"The texture we touched/felt was perfectly ....?...."
This book's full [unwieldy, not-picked-out-by-me] title is Try To Feel It My Way: New Help for Touch Dominant People and Those Who Care About Them, John Wiley & Sons 1997.