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—you may have many worries weighing on your mind—hurry is not: it's a quality ascribed to persons or activities rather than an instance of hurrying.^†

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—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".

^† _{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.}

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—you may have many worries weighing on your mind—this is very rare with hurry: it's almost always a quality ascribed to persons or activities rather than an instance of hurrying.^†

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—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".

^† _{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.}