You can choose not to use propane. The stove can be covered and you use a hotplate in its place, microwave will still work as normal.
Water heaters can be propane or gas/elec. If you can run it on elec alone will depend on the unit, but it will not heat water quickly in electric only mode. There are small electric tankless water heaters for about $150 that may be able to replace the one in whatever trailer you get.
You can make the changes, it may not be as convenient as originally designed, but it is possible.
With the limited budget you may want to find the trailer and use gas the first few months until you can gradually change out the water heater or buy electric griddle or hotplates.
Trying to go "all electric" may tax your trailers electric system, if you get a 30 amp service model, an AC unit will be using about 14, a hot plate can easily use 10 more, you may find yourself constantly turning things off to get other things to work without tripping breakers.
Good luck.