Interesting to see on the link that John Lee Hooker & Canned Heat worked together, since the two songs in the OP also both sound like Canned Heat’s Fried Hockey Boogie. I think there’s a general Boogie thing going on here (but it’s more than that – Shake Your Hips and La Grange are really, really similar.)
Surely the Stones themselves credited “Shake Your Hips” to Slim Harpo, didn’t they? Or is this a case, like “Love In Vain” and “Prodigal Son,” where some copies of the record credit the original source and others don’t? I’ll have to check my LP and CD when I get home.