Is there an easy way to manually cut out loads without the use of high-end editing software? I know there's plugins that precisely time YouTube videos but I can't find any that let you specify load times.

Nope not really. Is it a PC game? In that case consider looking into writing a load remover for it.

It's an older PC UE3 game with basically no documentation. I'm assuming that would require using a memory viewer and I can confidently say from experience that I suck at it.

someone in the nsmbw community has made a windows program to retime loads out of their runs. it works for any game but is 100% manual and tedious. https://github.com/RootCubed/LoadRetimer

but you can always commision someone to make a load remover/autosplitter in the speedrun tool developement discord https://discord.com/invite/N6wv8pW

or you can make it yourself. its a fun "puzzle" to figure out how it all works though ive heard UE is a bitch but people in that discord can be really helpful even if intimidating