Measure the top and bottom panel and 2 shelves and mark where you want to cut. Use masking tape along the cut line to reduce splitting.
After cutting, sand down the cut edges.
As for recreating the dowel holes, that will depend on your woodworking skills. If you do not feel confident about it, then just screw the frame and shelves in, after determining the best height for your books. You can always cover up the holes with the VARIERA cover caps.
I can’t be sure but you may have enough scrap material from the discarded pieces to create a toe-kick for the front and back of the cabinet. This will help prop the wall cabinet to the same height as your METOD base cabinet.
Then just slide the cabinet in and caulk the edges if you want a more polished finish.