寝ちゃわなきゃ is a very contracted form.

Starting from the fully expanded version, this developed roughly as:

• 寝【ね】てしまわなければ
• 寝【ね】ちまわなければ
• 寝【ね】ちゃわなけりゃ
• 寝【ね】ちゃわなきゃ

I presume you understand the ～なければ + いい construction, so I won't explain that here.

寝ちゃわなきゃ is a very contracted form.

Starting from the fully expanded version, this developed roughly as:

• 寝【ね】てしまわなければ
• 寝【ね】ちまわなければ
• 寝【ね】ちゃわなけりゃ
• 寝【ね】ちゃわなきゃ

I presume you understand the ～なければ + いい construction, so I won't explain that here.

In response to your comment. :)

～なければ is what you get from ない + conditional ～ば, and it means "if ～ isn't the case / if ～ doesn't happen". So ～なければ + いい means "it's good if ～ isn't the case / if ～ doesn't happen". When you're talking to a person, this can sometimes be translated as "you shouldn't do ～".