Better to use something to get the clog out rather than something which will put the clog in your greywater tank. Most clogs are due to hair accumulations and they can hang up on your drain valve if they make their way to the tank. I found that out the hard way!
Shower clogs are usually in the P-trap area and can be pulled up out of the drain with the proper tool. Try searching in Amazon for "drain snake" and you will find many possibilities. I have been very happy with the Drain Millipede (
https://www.amazon.com/FlexiSnake-Dr...gateway&sr=8-3).
Tim