Instead of linking to the actual file, you can make your download links something like:
example.com/download.php?file=1.zip
In download.php script, you will just set the correct headers to force a file download, like:
header("Content-Description: File Transfer");
header("Content-Type: Application/Force-Download");
header("Content-Disposition: Attachment; FileName=...your filename...");
header('Content-Length: ...file length in bytes...");