That works. I'm a native English speaker, and I've said that sentence on multiple occasions.
I've always done it that way.
I've heard this version moderately often, and I've used it a few times. It's a little more generic.
I've always used it that way.
If you don't want more generic, this is the
used version of my first alternate example.
There are a lot of ways this could be said that would still be natural.
Going off-topic, while there are some shampoos that are designed specifically for hair, there really isn't a lot of difference conceptually from soap and shampoo. Humans are hairy enough in general that I don't think a soap that didn't plausibly work as a shampoo would be very popular hand soap.