Please cite the dictionaries that made this error. The Arabic words for wrist are معصم mi‘ṣam and رسغ rusgh. I looked it up in al-Mawrid by Munir al-Ba‘labakki and A Dictionary of Modern Written Arabic by Hans Wehr, and they all agreed راحة rāḥah means ‘palm of the hand’, not ‘wrist’.
Meanwhile the American Heritage Dictionary says racket<rasceta comes “from Arabic rāḥat (al-yad), palm (of the hand), bound form of rāḥa. See rḥ in Appendix II.”
“rḥ. DEFINITION: Common Semitic noun *rāḥat-, hand, palm of the hand (*-t-, feminine suffix). racket, from Arabic rāḥat, bound form of rāḥa, palm of the hand.”
The Barnhart Dictionary of Etymology says racket was “borrowed from Old French requette, rechete racket or battledore, palm of the hand (perhaps influenced by Spanish raqueta) from Arabic rāḥat, a form of rāḥa palm of the hand.”
The reason for that disappearing and reappearing -t at the end of the word: Arabic feminine nouns have an inherent -t sound in the ending, but when the word is cited in isolation, with a pause after it, the -t is not pronounced. So the ending -at becomes -ah in pausal form. But in the construct state (al-muḍāfah), when that ending is followed by a word grammatically asociated with it, the -t is pronounced. Arabic script writes this ending with a single letter ة called tā’ marbūṭah (‘bound t’), which has the round shape of the ه h plus the two upper dots of the smiley-face ت t, to show that it can have either pronunciation, depending on the position in a phrase.
Also, I think the etymology of racket in the sense of dishonest business can be traced to the same etymon, since dishonest business practices are symbolized by expressions like “grease someone’s palm,” i.e. pass money surreptitiously.