Jurassic Park is the best ride in the park, and I'd encourage you to try it out. If you're okay on Splash Mountain, Jurassic Park should be fine too.
Mummy is not a particularly high-speed roller coaster, although it feels scarier just because it is in the dark.
Now, if you're concerned about scary imagery, then there are a lot more scary attractions. (This can be the problem with taking young kids to the park.)
In Jurassic Park, you are attacked by dinosaurs, on Mummy you are chased by demons, and in Terminator 3-D it's robots. In Backdraft, the room catches on fire, and even the fairly benign special effects stages have a rather frightening monster. The House of Horrors is a scary walk-through haunted house.
The tram tour is mostly fine, but does have some frightening scenes - an attack by King Kong, a simulated earthquake, and a trip through the Mummy's tomb. (Depending on the day, the tram may skip one or more of these scenes.)
I hope that's helpful!
Mummy definately won't kill you. It's fun (too short, though).
Walt Disney World
Tokyo Disney Resort