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It's worth a go - check youtube for details - it's slightly fiddly but doesn't take long. Even if it's an odd size it looks pretty similar to what I've stripped. We had some descaler knocking about, but a good scrub and/or white vinegar probably also do the trick.
When you pull apart there are a couple of rubber seals along the way - one of them may have gone.
Gives you a good DIY satisfaction vibe if it works!
Have you tried taking that apart, giving it a good clean out and putting back together again? There'll be plenty of scale clogging things up in there.
I've done it a couple of times to ours and fixed the leak for another 6 months.