Hmmmmm.
An interesting POD. There might be some resistance from the Sjem, but I'm pretty sure that Sigismund II can overcome it. After all, there is precedence of Poland at least being inherited through a woman, Jadwiga springs to mind since she was the way the Jagiellons got onto the Polish throne in the first place.
Just browsing through Wikipedia, here are some of the more prominent potential grooms in the surrounding nations.
Hapsburgs: Sigismund apparently had a bit of pro-Austria bent to him, so it wouldn't be uncalled for for a Hapsburg to be a shoe in for the throne if Sigismund thought it was a good idea.
Charles_II_of_Austria
Don John_of_Austria (unlikely, since he was a bastard, but he's here for funsies

)
Archduke_Ernest_of_Austria
Mathias,_Holy_Roman_Emperor
Rudolf_II,_Holy_Roman_Emperor
Non-Hapsburg: While Sigismund may have been a wee bit pro-Austria, the Sjem usualy wasn't. So here's some others.
Stephen_Bathory_of_Poland (though he's nearly twenty years Sigismund's daughter's senior, he was king of Poland in OTL (married Sigismund's sister) and a good one at that.)
Joachim_Friedrich
William_V,_Duke_of_Bavaria
Of course, I really only listed potential heirs to the throne of neigbouring kingdoms, and Sigismund/Sjem might go for something that wont entangle them in foreign wars and such, so you might see the brothers of the heirs get to marry into Poland. At this moment I didn't have the time to look up any brothers to most of the Hapsburgs or German princes.
Then again, there is always the Russian connection.
There is the of having
Fyodor_I_of_Russia marry his daughter. The problem with Fyodor was that he was reportedly mentaly challenged and never had any kids. If she and Fyodor, Russia could actualy be possibly brought into the union, ending Poland and Lithuania's eastern border problem. This probably doesn't really help the POD since he might not have been able to have kids leading to the extinction of that line as well.
Then again, you could just bypass Fyodor and have Sigismund's daughter marry
Ivan_IV. Though too young to be Anastasia's succesor, Ivan could potentialy marry her after the death's of either Maria (died 1569) or Marfa (died 1571).
Perhaps better, you could have Ivan's other son,
Ivan_Ivanovich (the son he beat to death) marry Sigismund's daughter. They were even born in the same year.
Ivan IV was held in pretty high regard by a fair amount of Polish nobles, so you might see an interest in the Poles of having the Ruriks become the new kings of Poland and Lithuania. If the Ruriks were to come into power, Russia could actualy be possibly brought into the union, ending Poland and Lithuania's eastern border problem.
This kind of union would be far different from Russia's eventual conquest of Poland-Lithuania, with Poland and Lithuania having quite the cultural influence on Russia.