There are no such inappropriate 'Straight Shota' stories in the official Dragon Ball Z canon. Dragon Ball Z mainly focuses on epic battles, power-ups, and the adventures of Goku and his friends to protect the Earth from various villains.
Dragon Ball Z is both anime and manga. The anime was adapted from the manga and they share the same story and characters, but presented in different mediums.
One alternative is to focus on character backstories. You could write about the early days of Piccolo, how he came to be the way he is. Another option is to do crossovers with other non - sexual universes. Maybe a story where the Dragon Ball Z characters meet characters from a magical anime world and they have to work together to solve a problem. Also, you can write about the relationships between the characters in a platonic way, like the deepening of the friendship between Gohan and Krillin.
A Kryptonian in the Dragon Ball Z universe could potentially be a very powerful addition. Their natural abilities like super strength, flight, and heat vision could make them a force to be reckoned with. However, they would also face challenges as the Dragon Ball Z world has its own power scale with ki-based powers. They might have to adapt to the different fighting styles and power sources. Maybe they could learn to use ki in addition to their Kryptonian powers, or they could find a way to combine the two in unique ways.
Goku is, without a doubt, one of the most popular. His constant pursuit of strength and his ability to overcome seemingly impossible odds make him a favorite for fanfiction writers. They can create all kinds of new adventures for him, like facing off against cosmic threats even greater than what he's encountered in the shows.
One interesting crossover could be a battle between Hulk's brute strength and Goku's Super Saiyan power. Maybe in the fanfic, they start off as rivals, with Hulk misunderstanding Goku as a threat to Earth. Their fight would be epic, with Hulk's limitless rage against Goku's increasing power levels. It could also explore how their different universes' power systems interact.
One interesting fan theory is about the potential hidden powers of some minor characters. For example, some think that Yajirobe might have a secret super form that was never revealed in the original series. It's just a fun idea that fans like to explore in fanfiction.