Good question. Maybe England would become a republic like the Netherlands instead of trying to sort out the succession?
I doubt the English would ever go for a true Republic over the Constitutional Monarchy that was being set up even in William and Mary's time. I mean, if the monarchy and the House of Orange could live through Leopold the Traitor (reign:1834-1843) and his noxious sons for over 30 years all the way to Frederick The Great (1876-1903), when other European nations went through bloody turmoil during the 'liberal revolution' (generally accepted as starting with the Paris uprising in 1828 and ending in 1864 in the 'Year of Blood'). I'd say the Oranges are pretty well entrenched, which is a good thing for the UK since, as the only nation which retains a 'functioning' nobility in Europe, it rakes in boku tourist and 'entertainment' pounds. I mean consider Mina's Jubilee... by all accounts, the biggest, most expensive party in the history of the world. Parliament allocated 700 million pounds to it... and by the current accounting they have raked in well over 10 billions pounds... a return on investment that has made the Republics of Europe green with envy and grumbling at their ancestors who were too overcome with revolutionary fervor to see the moolah.
As for the OP, The English were certainly not above shopping around the continent for a Monarch as the Orange family clearly represented. Parliament was very anti Catholic at the time, and wouldn't have abided a Catholic monarch. So they would have gone shopping in Northern Europe, most likely Germany. I doubt they would have gone for a Hohenzollern though, since the last thing the UK needed was a monarch with strongly divided loyalties (which is a big reason why Parliament passed the 'Renunciation Act' in 1724 before William III's coronation*)
*OOC: Queen Mary II lives a lot longer
Now, as for alternatives to the Oranges, while I'm kind of rusty on my 'Somewhat Obscure German Protestant Nobility'

I do know that, of all the Federal German Republics, Hanover has the most ties with England since Sophia of Hanover (1630-1718) was the granddaughter of King James, and her son, George, lived FOREVER and had tons of kids aka a direct line from the Stuarts. If the Oranges hadn't worked out for England I can see Parliament looking at Hanover, which has always been a small place squeezed between the great city state of Hamburg and the trading monstrosity that is/was the Netherlands. I doubt, Sophie, or George (depending on who died when) would turn down such a choice offering as being King of the UK...