Since you can’t install the sync client, you may want to explore using the built-in Windows WebDAV client. It allows you to map your NC data to a drive letter. There are some limitations/caveats but works well unless your files are >50MB routinely or you have poor connectivity.
Out of curiosity, what types of files are you manually moving around? If they’re Office files or something like that, you could activate server-side Nextcloud Office.