Word for a playing card that isn't a Joker?
Solution 1:
How about suit cards?
The jokers are distinguished by not having a suit. And this phrase has been used for exactly this purpose (Google fifty-two suit cards).
Solution 2:
A deck of cards consists of fifty-two playing cards plus two jokers. Jokers, whether there be one or two, are not counted among the playing cards. Jokers only appeared in decks on or around 1860 when a version of euchre became popular in America that involved a third bower, which is why there are only two jokers and not four. Even the name joker is a permutation of euchre. The joker is not standard fare in card games, not even in euchre.
Short Answer: The word for a playing card that isn't a joker is "playing card." Jokers aren't playing cards.
https://en.wikipedia.org/wiki/Playing_card
Solution 3:
..and fifty-two non-jokers :). Hehe, and why not say 'and fifty-two regular cards'.
Or: A deck of playing cards usually consists of fifty-two cards and often two extra joker cards.
Or: A deck of playing cards usually consists of fifty-four cards.
And then split it out in the rest of the story.
Solution 4:
A natural hand is a hand without any wild cards. So perhaps you can say non-wild cards are "natural cards".