I have heard of riders finding tires in Panama but it seems to be a bit rare. You may be better off waiting until you get to Colombia. Should be a several choices of tires in your size there.
Not sure you will find Shinko but other brands that may work for you. Lots of bike support in Medellin.
I don't know any contact info on shops in Panama, but I'm sure there are some. No idea what tires they have on hand.
Post up here asking for tire source in Colombia, I'm sure you will get some response.
Buena suerte,
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