Compatibility of mounts and tripods

[Mandopicker101]

I'm looking to buy a new tripod for my EQ-1 mounted Celestron refractor. Great OTA, mount's OK but the tripod is knackered (it was an unbelievable Gumtree acquisition - £10 for a Powerseeker 80!). The optics are great but viewing is compromised by a tripod that you need only look at to make it shake. I've eaten Blancmange with greater solidity.

I'm looking at a couple over on Astroboot and there's a fairly solid-looking SW tripod but it's for an EQ-2 mount that sounds robust and well-priced. Would the bog-standard Celestron EQ-1 mount fit the tripod as is...or should I also add an EQ-1 tripod head as well to the order?