Finally someone that uses the LM386 as the output amplifier it is designed to be 
EDIT: Or not, see below 
Looks fine to me (I mean, it’s a rather minimalist design, so not much to complain about 
), so if you’re happy with how it performs on breadboard go ahead and build a more permanent version.
C3 is perhaps a bit low but to calculate the right values for a boucherot cell you need to know exactly what speaker you’re connecting it to, which seems like overkill 
(or is it a bit high, the datasheet says 50 nF?)
C4 is larger than I’d expect, the datasheet has 250 uF there and looking at the usual suspects (ruby, little gem, noisy cricket, etc) 47-220 uF seems common, but a big one is probably ok too.