Yes, problem of limited disk space affects a lot of designs. You won't be able to do this via Windows Update. Here's what you need to do:
1. You need to (at least temporarily) add a 32GB (or larger) SDHC/SDXC flash and choose it as destination for user and application files.
2. Download ISO image for full OS install and make a bootable USB installation flash (Microsoft provides tool for doing this).
3. With Windows running, insert this USB installation disk and start the upgrade process using its provided Setup.exe file.
4. (Important!) When asked about downloading any additional updates, say NO (we will do these later via Windows Update process).
5. If asked about disk space, point to SDHC/SDXC flash.
6. Let upgrade run. Should work without error.
7. Once completed, use Disk Cleanup app, with System File cleanup enabled, and add checkmarks to cleanup everything. You, this will delete downgrade files, but you will need the space to apply subsequent updates.
8. Run Windows Update and install all available updates. After finished and system has rebooted, run Disk Cleanup app and delete aggressively again.
That's it. Should work. I have updated multiple NUCs, Compute Sticks and Windows Tablets using this process.
Hope this helps,