With the current version of uTool re-exporting the playlist you need to have enough space on the drive for the playlist and the included songs as well.
You can see the required free space on the drive when you select the playlist, then you click on the multitrack tab. If the free space on the drive less the export button remain grayed out. I know, you want to export the playlist only but unforutately the current uTool version check the available space for the playlist with the songs. We’ll change this in the coming uTool version.
You can export the content to your local HDD then manually copy and replace the playlist from the local drive to your external HDD with file explorer.