No need to swap the Game Boy Player case - the GBP is region free - it's just the disc that causes the issues.
You can use the JPN Disc on a JPN Cube with a US Game Boy Player or a US Disc on a US Cube with a JPN Game Boy Player.
Or, with the Freeloader, you can use a US Disc on a JPN Cube with a US GBP or a JPN Disc on a US Cube with a US GBP. Or a US Disc on a JPN Cube with a JPN GBP. Or a JPN Disc with a US Cube on a JPN GBP.
Make sense?
Regarding the Freeloader - You'll probably have a slightly easier time getting a GCN Action Replay - they have a Freeloader built in. Grab one of those with a Datel/AR-branded memory card. Now, copy the Action Reply files from the AR-branded card to a cheap-o used official Nintendo memory card 59 and junk the Datel one. They're flaky and not trustworthy - but if you don't copy it over and it goes out, your AR is now worthless.