[FAQ] Shiratamako is a processed rice flour made from mochiko which is sticky rice (sweet rice). In North America, they sell a product called Mochiko and this flour is made much simple than the Shiratamako, but is from the same kind of rice, it should work, but you may not be able to get the silky surface when boiled.
In Asian markets, it seems they also sell other rice flours. I do not know what kind of rice they use to make the flour and unless you see a word such as "glutinuous", it may not work.
When making the dango, please be careful with the amount of liquid you add into the flour. Depending on where you live (humidity), you may need to add more or less. The key is to get the texture like your earlobe..soft but just firm enough to make the balls.. Good luck!