I'd test the waters and see what I could get. Although, if I couldn't get a stud in return I wouldn't bother. Remember, even though you are punting saves, you can always add dominant setup men to replace them. These guys may help you more in ERA, WHIP, and K's than a mediocre or below average closer ever would. In your case, Guardado (if he can stay healthy) could be a really good closer, Wickman probably won't be too friendly to your WHIP and ERA.
No strategy is perfect, you just have to find out what works best for you. I personally decide as the draft unfolds. If closers are going too early for my tastes, I bolster my offense and starting pitching, and then grab dominant middle relievers late. Works for me, but maybe not for someone else.