We all know Blackbeard is an opportunistic machiavellian character. He also is aware of the recent developments in Wano.
This leads me to think that Blackbeard has his eyes set on Whole Cake. After all:
-Whole Cake won’t be as protected as usual.
-In this place (Whole Cake Island) there are several Poneglyphs, including one of the four leading to Rafael.
-A lot of Big Mom’s subordinates (even the weaker members or the younger children) have Devil Fruits which we know are also a target for the Blackbeard Pirates.
Even if Teach does not send a huge military power to Whole Cake Island, now we know that in his crew there are two captains with skills which are perfect to infiltration missions: Shiryu (invisibility) and Devon(Kyubi=Shapeshifting), which will make a lot easier to steal the Poneglyph.
After that, Blackbeard will show up in Wano at the end of the war where every one is weakened, take Kaido’s Zoan devil fruit (like he did to Whitebeard in Marineford) and take the Poneglyph there as well, giving the Blackbeard Pirates a headstart on finding Laugh Tale.
Blackbeard has shown himself to be an expert planner and a master at orchestrating manipulative schemes provided he has a sufficiently advanced period of time to prepare. I think Wano will be no different.
*Theory by efegoforit