This guide concerns GBA SP. About GBA, I never tried so I can't help (but I guess it won't be so different). About DS, I can't try again cos I don't have the good cruciform screwdriver. Nontheless, principle is the same, and you can find some guides on the Net (a French one with pictures ; you can make use of it ).

<--- the stuff : a Triwing screwdriver (to dismantle GBA SP) and a file to shave the cross

6 screws have to be removed. The battery's screw (6) can also be removed with the Triwing (at least I can) ! Otherwise, use a little cruciform screwdriver... The (5) is different ; put it aside.

Then, take off the battery...

You can see a 7th screw to remove. As the 5th one, it is different, be careful ! After that, take off the... "cover".

Have a look behind the cover : there is a nut. It's possible it falls when you'll take off the cover. If so, put it as in the picture. Without it, you won't be able to close the battery's lid (with screw (6) when you'll put together again the GBA SP) !

OK ; now look at your GBA SP ! It's the board (dunno if it's the good word with my crap English...). 3 new screws have to be removed. Once again, I can do it with the Triwing. Otherwise, use a cruciform screwdriver...

Raise the board : the end is close ! Cross direction is just under this plastic stuff ; remove it.

Take the cross and look at underneath. This bump at the middle is the problem ! File it, shave it, do what you want to shrink this bump !

Be careful to not shrink it too much, otherwise it'll be unplayable ! I think mine was a little too much filed, so this is the smallest size to not exceed.

After that, do all the stages upside down, and test ! Trick : when you'll put back the board with the 3 screws, turn over your GBA SP and press at the same time left and right on the cross... If you feel the entire cross sinks, that's OK ! Otherwise, if the bump still hampers, file again a little... Successrate is always 100% when it's done properly. So if it's doing wrong when you're playing, file the cross again cos it can be the only problem...

Easy

I have my DS lite pro-ZZMT

It was an hard and risky work for me (i'm not expert of this kind of operations) and i had to insert the motherboard of my old broken DS lite in the new one, because i broken the power on piece of the new one.
It was a problem even to reinsert in the right way the shoulder buttons... but at the end i did it.

The first 3 minutes of the following video are enough to access the crosspad.
(remember, as KartSeven said, do not shrink it too much!)
http://www.youtube.com/watch?v=vRzTgfo2PsM

Anyway i suggest to use a GBA SP because is cheaper and easier to reassemble.

Big bump, but I made my own little twist on this guide to accomplish it so enjoy!