First of all you have to define "expat" as many foreigners in Panama come here from South America (mainly Colombia) and are indistinguishable from the Panamanians to the Gringo eye.
I am asked this question all the time because I run the News.Boquete email distribution system which delivers local news and events to the English speaking population in Boquete. I was even asked the question by the U.S. Warden for Boquete. The answer is that nobody knows. There are nearly 1500 subscribers to the News.Boquete email list but many people don't subscribe, husband-wife teams often have only one subscription, and a few folks not living (yet) in Boquete also subscribe. If I had to guess, I would say there are 2,500 - 3,000 English speaking expats living in the district of Boquete which includes the greater Boquete area and even the city of Caldera.
I thought I remembered a question on the 2010 census asking in what country was your mother on the day you were born. That statistic would tell us something but so far the Panama government hasn't published the totals.