After updating the LA portable version, it won't start.

[Gintaras]

Can I now just drag and drop the "files" folder from the old version of LA into the file list for import?

Try. Exit portable LA and replace \files. Should work if portable and non-portable workspaces are similar.
 

I only want to update files, excluding the "files" folder and "files.xml,"

The portable LA setup tool can't do it. Use some other way to copy these files. But updating \dll without updating script files is not recommended.