Yes you can trip the breaker in the 110V panel.
There is 12V power source and 110V power source that comes into the hot water heater. The 12 volt circuit is shown on Figure 7 of the manual (page 4); the 12V hots are 18 AWG red, common is black and ground is yellow. If you shut the hot water heater propane switch off, this will disable the 12V circuit as well.
For me, I would wait until tomorrow AM, say sunrise when it is cooler?.
Earlier I mentioned you may want to completly shut off the water heater (electric and propane) and open a hot water tap in the trailer until it runs cold. Then turn off your campground water tap, and open a tap in the trailer to reduce the water pressure in the system (leave it open until you finish replacing the element).
For start up, work backwards making sure the new electrical element is not turned on until all of the air is out of the system - ie turn on campground tap, check for leaks around the heater, open a tap in the trailer until a steady stream of water comes out the hot tap (ie no air). The new element will crater if you turn it on with air in the hot water tank.
Dave suggested putting a water based lubricant on the seal of the element before you tighten it down. Good idea - I usually just use spit, but any water based lubricant is fine.
Hope this helps.
Take care,
Brian