Should I be worried about mosquitos and yellow fever walking into that park?
Not anymore than in other places in Panama. I have never had to use a mosquito repellent while going there, but I usually use long pants and long sleeve shirts, since you're walking in a tropical forest the insects besides mosquitos may be attracted to you...hahaha
I am so sorry to be late in seeing this question and answering it. No, this area in Panama was cleared of Yellow Fever decades ago by the former American "owners". There were very few mosquitoes or other insects that bothered us during the dry season, when we visited.
Get quick answers from Soberania National Park staff and past visitors.