So if you're not using a mod manager, does that mean you're manually installing everything? That seems like a lot of extra work to me.
To answer your question, your best bet is probably going to be to create a backup folder somewhere else on your computer, cut (not copy) and paste everything from your Fallout 4 install directory into that folder, then verify your Fallout 4 install via Steam. Once it's finished reinstalling everything, install only the mods you need for the City Plan Contest. When you're finished building your plan for the contest, you can copy and paste everything from your backup back into your Fallout 4 install directory, and in theory, all your mods should be back and working as you intended. As an added bonus, this kind of gives you a restore point if a future update breaks your current setup.
With that said, I would strongly, strongly encourage you to start using a mod manager if you want to take part in the contests. If you're always installing stuff manually, there's a high risk of something getting missed or not properly disabling unless you use this drastic "nuke it and start over" approach every time you want to switch from modded play to contest entry construction. With a mod manager, however, you can set up profiles that allow you to reduce this changeover to a couple of clicks and a few seconds of waiting while it redeploys your mods. My understanding is that Vortex can handle loose files as well as other mods, and I know from experience that it can package and deploy mods from your harddrive as well as ones you download from Nexus using Vortex itself. As a matter of fact, that local install used to be the only way to access the Wasteland Reconstruction Kit's predecessor, Project Blueprint.
Either way, I hope you do join the City Plan Contest. It's always cool to see more takes on the themes and challenges we're presented with.
Only four days until we get to know the new settlement, though, so I'm quite excited.