I do have a fairly simple solution to this.
I had purchased the Opera Web Browser for my ds lite back when I did not have my M3DSR (Rumble + GBA Expansion) yet. After I got my Rom cart and found out that I could get Opera to work with my GBA Expansion memory I got tired of switching between the actual cart and the rom cart. Thus the real cart became useless...for me at least.
Now, since I have a DS Lite I no longer needed my DS Phat so I gave it to my little sis. Eventually she asked me if she could have my extra Opera cart that I'm not using anymore. I was like, sure, but one problem....DS Lite RAM Expansion card instead of a DS Phat RAM card.
I tried to take it apart and just use the board like
tedmg09130913 suggested, but it's very difficult to unscrew a tri-wing screw with flat and phillips head screw drivers.
The solution to this problem was simply to file away the extra nubs/tabs on the side of the cart and to file away the groove on the face of the cart that makes it easier to remove from your ds. All I did to it after that was to put a kind of tab on the back of the cart that was made out of duct tape so that I could still remove it after I had it shoved into the DS Phat.
All together, once I figured out what I was going to do, it took about 10 minutes (using crappy files) and it works perfectly and no damage or modding was done to the actual system.
I suggest trying it out, It should not hurt anything.