IANA business or marketing insider, so I can't vouch for industry jargon. But purely from the POV of the average person, I totally agree that "stray" is _not_ the right word, for exactly the reason you cited: It gives the impression that the customer has slipped his/her leash. (-;
No single one-on-one match occurs to me. But for the Kunde/-in part, you might also consider shopper or buyer. To me, the word customer itself connotes somewhat _less_ casualness. Along a spectrum of intentionality, customer might be more toward client or patron, someone who gives a name, makes a reservation, etc.; whereas a shopper just walks in off the street. (Restaurants being one exception; there you'd have to go with diner or something.)
For Gelegenheits-, casual seems reasonable, or perhaps occasional. For a more spur-of-the-moment decision, perhaps more toward your original "whim" and Manu's Zufalls-, what about walk-in, or impulse?
Casual shopper, impulse buyer, walk-in customer... Maybe a web search on various combinations of those will turn up something that fits your context.