Falscher nominalisierter Infinitive ohne Bindestrich/getrennt oder falscher Imperativ?

Question

In the kitchen of the place where I work, there is a note next to the paper towel dispenser:

• Sparsam verwenden! (use economically)
• nur zum Hände abtrocknen (only to dry hands)
• nicht das Geschirr abtrocknen (do not use to dry dishes)

where the English version is also attached on the note (in brackets). I am not sure if it was hung there by a native speaker, as I have some doubts to the correctness of the above. These just sound wrong to me, and based on the rules I have been learning - could be structured incorrectly.

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Let me start from the second bullet point - if this is interpreted as Imperativ (Sie) due to abtrocknen starting with a small letter, I think it should read e.x.

1. nur die Hände abtrocknen, or better, proper Imperativ style
2. abtrocknen nur die Hände

In other words, zum should not appear there at all.

On the other hand, if zum is to remain, then consistent with the Dativ declension, it suggests that abtrocknen appears there as a nominalised Infinitive, therefore as das Abtrocknen. In this case, it would need to appear together with Hände like the following:

3. nur zum Händeabtrocknen

Alternatively, if zum is to be used:

4. nur zum Abtrocknen/Trocknen der Hände

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The third bullet point also looks weird to me. I would write it as:

5. Abtrocknen das Geschirr (damit) nicht (Imperative style)

or, following the zum style of the previous bullet point

6. nicht zum Geschirrabtrocken / nicht zum Abtrocknen des Geschirr(e)s

I would be grateful if you could comment whether my observations hold and additionally, if the replacements I'm suggesting (1-6) could work.

Answer 1

1 and 3 are examples of impersonal imperatives. This doesn't exist in English so it's hard to translate, but there is no subject and the verb is just a bare infinitive placed at the end where infinitives normally go; there is no finite verb. It's often used where no one in particular is being addressed, and a public sign like this is a typical use for it. I think 2, much like its English counterpart, is not a complete sentence, so you have to fill in some words for the grammar to work. It might help to tack on "verwenden" to make it another impersonal imperative. I think you're right about the capital letter though. The wording seems very "informal" to me, convey the information in as few words as possible and let the chips fall where they may when it comes to grammar. But the impersonal imperative is a legitimate sentence form. For some reason grammar texts don't cover it as much as they should.