If you wanted a Project that is 4K to be smaller, let's say 1080 for example, you'd Duplicate your 4K project, give it a new name. Then with it selected in the Browser, go to the Inspector, and there you'd click the Modify button and change the size to 1080. You may need to move titles and such around. But that's about the quickest, easiest way to do it.
If you're simply cropping clips in your 4K project's timeline, you're still working in a 4K resolution. Cropping clips does not change the resolution of the Project.
You could also export via a Compressor preset that you create. Duplicate the preset that you were using, rename it and then go under the VIDEO tab and change the Frame Size to what you'd like. One thing to note is that at towards the bottom of this tab are some resizing options called "Quality". Linear is default and in most cases that's fine. Nearest Neighbor is fastest but it can give you some nasty artifacts if you're not scaling in perfect integers.
Another thing to note is that you have to manually add this export option to FCP, it doesn't automatically see what you have set up in Compressor. In FCP, go to Preferences, Destinations... choose +Add Destination, click Compressor Settings, scroll through the list until you find the preset you just created. Now in FCP export your 4K timeline through the new preset by selecting the timeline and choosing File > Share > Your new preset. If you make changes to this preset in Compressor, I believe you have to re-add it to FCP for the changes to take effect.