*Neither hurries nor worries* doesn't to my ear have the sort of rhythm you want in a catchphrase. And although *worry* is commonly used as a count noun&mdash;you may have many *worries* weighing on your mind&mdash;this is very rare with *hurry*: it's almost always a quality ascribed to persons or activities rather than an instance of hurrying.<sup>&dagger;</sup> 

*No hurry, no worry* sounds better to me. It might have two meanings, depending on the context:

* There is no need for your hearer either to hurry or to worry&mdash;you don't need immediate response or action. In other words, "Don't hurry, and don't worry".

* Your hearer should avoid hurrying, because that will avoid future problems. In other words, "If you don't hurry, you won't worry".

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<sup>&dagger;</sup> <sub>Except in US football jargon, where *a hurry* is an instance of transitive *hurrying*: rushing the quarterback so aggressively you compel him to pass the ball before his receivers are in good position to catch it.</sub>