from my limited understanding of discernment, if there are no Catholic options, that in itself could be a clear sign from God: He feels you are ready to accept the challenge of working in a secular workplace exposed to lax morality.
to me, there are two fantastic reasons to work in a non-Catholic hospital: evangelisation and testifying. now, i do not mean go around condemning ppl - i think here ppl understand Catholic evangelisation as being a model Christian and allowing ppl to be drawn to us by our loving example. testifying, however, would be somewhat less passive - in that you speak up when moral infractions are committed. there are different levels of being active in testifying too: you could be the type who will speak to ppl-in-charge (aiming to effect change at higher levels of management) or you could simply be explaining to your fellow colleagues why you think abortion is wrong (simply being informative). you could also gather fellow pro-lifers to pray for aborted babies everyday. these are some very great things that could potentially be done even in non-Catholic hospitals - of course, they can also be done in Catholic hospitals where needed.
the crux being that being so sure of your faith and living it out so tangibly outside the shelter of a Catholic environment requires a good prayer life and possibly a spiritual director whom you meet with regularly. if the circumstantial signs point to the secular hospital as the best choice for employment - whether there’s a choice or not - the challenge to strengthen one’s faith life is still a constant. but if you have to face a greater challenge, do make sure you are prepared!
for instance, you’ll have the prayers of this forum, i foresee… =) the Lord bless you and keep you, no matter where you choose to work!