That's tricky one.
Possible option (though little cumbersome)
Before you begin the below process enable bluetooth on your mobile and also on your laptop. Pair them up so you don't need to click "yes" every time.
1. Open your browser --> Menu --> More --> History
2. Long press on a link and click on Share Link --> Bluetooth.
Repeat above process to at least transfer your favorite links.
You can also use Share Link --> Gmail or other options available there, but I think bluetooth is the quickest method.
Can't think of anything better.
Perhaps the history is stored in some file on your phone, so try to explore files on your phone with ASTRO etc app and see if you can transfer that file instead.
Cheers.
