They won't. They'd have to license the format from Sony. Thus giving Sony money. Nintendo isn't going to do that.

I think they'll go for an SD card-like cartridge.  Sorta like the DS ones but higher capacity of course.

So, if they wanted to use Blu-Ray on Wii's successor, they would have to do the same?

UMD are virtually dead, the only support for them is the PSP so why bother with an almost dead format?

Not happening, sorry. Nintendo will stick with cartridges, and my guess is that they'll be the same size chip input as current DS carts, so that the DS2 can maintain backward compatibility, but I see them maybe being T-shaped, so that DS2 carts won't fit into a DS?

Pretty much.

so you want them to add a redundant prepritary format that has no advantages over Flash memory based media and adds cost and battery drain onto their next handheld (UMD drive) plus would increase load times (flash based has no seek time and could have faster transfer speeds)?

No Nintendo won't move to optical media for the DS2

PS nintendo would have no problem paying Sony to use a format if the format benefited them. and little to no money the would pay for Blu-Ray would go to Sony. 

They'd license it from the Blu-ray Disc Association which diversifies the license royalties out to member groups though Sony gets the largest share.

I fully expect their next portalable and home system to utilize flash memory medium for its physical games.  Or possibly a proprietary non-standard disc medium.

Nintendo will never go both digital (fully) and UMD

Nintendo will use cartridges and digital for the next portable, like DSi, and some proprietary disc for Wii 2, just like mini dvd's on Gamecube.