Don’t do that: it will just burn up.
How much current do you want to use? For 2.0A to 2.5A you could build a Knucklehead v3.0. See here: Mattaus - Knucklehead Buck Driver Discussion Thread Mattaus has removed the OSH Park listing because of the driver’s inability to handle his 4A design goal reliably (at least unpotted), but RMM has tested the driver to be fine at lower currents like 2A. I’d send Mattaus a PM, but if you can’t get in touch with him lots of us have the appropriate files, myself included. If you want to order boards you’ll definitely be able to.
How much space do you really have? The commercially available ‘thin’ options I know of are the two boards from LDCH, LD2C and LD29. The LD29 is ~18mm or ~19mm but uses a 20mm or 21mm contact board. It’s also still taller than 5mm. Also both drivers provide a little too much current probably without a resistor mod for a lower current.