If Cyprus is still around then they will probably be in a trade league and if that is Lubeck's trade league then you might be able to get a CB against someone in that league which you could use to take Cyprus. Same applies to the Knights.
Otherwise, there's always the no CB option to get a base down there. The Christians won't care that much and if your no CB war is just over Cyprus then there won't be too much AE with anyone.
I think Knights is still around but Cyprus had collapsed after a separatist revolt and got annexed into Byzantium who I happen to be allied with. But that's a good thinking right there. I've also forgotten about a possibility of a CB war with a country with whom Knights is allied with. Once that country honored the call to arms, I can then use this opportunity to seize Rhodes to fabricate the claims upon Egypt. I already possessed the strongest navy in the world so it's no problem for me. ;p
Also, if Spain is allied with Knights as I've seen sometimes in past games, I can use Colonialism CB for that. But that Spain option is sort of ruled out because it is also allied with Savoy, one of my other allies unless Savoy is tied down in a war and would dishonor the call. I think at this point, Spain is also allied with Ottomans but that is not a big problem (yes, Byzantium and Ottomans still co-existed by 1650s.... because I guaranteed them both ;p).
Also do note that at this point, England already effectively dominated the India with numerous provinces along with vassals so I had well over 10 divisions of my own in India along with sizeable transport fleets along with vassals that can open eastern front if Ottomans were to honor a CTA with Spain while opening a western front. Should be interesting if that happened.
I also can't use Call Crusades as England had converted to Protestantism due to Act of Supremacy event and thus effectively ruled it out as a possible curia controller so it is kind of too late on that one. Something I should've thought of when I managed to control the curia at one time while still Catholic.
At any rate, I will keep that Cyprus thing in mind next time I make another England run. Thanks!