It’s not really a matter of what to put after “utiliser” and more about what to use before “micro-ondes”

Examples (explained later) :

“Utiliser à des fins scientifiques” = “Use for scientific means”

“Utiliser avec des gants” = “Use with gloves / while wearing gloves”

“Mettre au micro onde” = “Put in the microwave”

“Mettre à la poubelle” = “Put in the bin”

TOPIC 1 :

1. “au micro-ondes” gives a very natural and correct feeling, it’s most likely what would be used by native French speakers to say it , so the translation is perfect as it is.

2. On the other hand, you would never ever say “utiliser à un micro-ondes”.
   It would sound very unnatural and just wrong.
   “Utiliser à…” would rather be used with a condition : “utiliser à une température de XXX / utiliser à la place d’un four” = “use at a temperature of XXX / use instead of an oven”.

Or even “at a certain place” : “utiliser à la plage / utiliser à New York” = “use at the beach / NY”

but never “utiliser à [an object]”

3. “utiliser dans le micro-ondes” would be understandable but would still give a feeling of foreign translation somehow, it sounds a bit unnatural but really not that much. It’s just a bit heavy/redundant sounding somehow.
   “Utiliser dans un micro-ondes” would feel a bit better but still not natural…
   As I said earlier “utiliser au micro-ondes” was already perfect, anything else would sound less natural.

4. French nouns are gendered (“une chaise, un tabouret” = “a chair, a stool”) and in some cases (like “micro-ondes”) the same word exists for both genders but with a different meaning.
   Here it’s either male and an object used to heat food up, or female and is a wave of short length.
   There is no real equivalent to that in English (as there is no equivalent to the a/an difference in French).

(again, “utiliser à un micro-ondes” doesn’t really mean anything, it wouldn’t be used in French and would be considered a grammar mistake)

TOPIC 2 :

French often requires some kind of object

It’s not always true indeed… you could say “je sais !” , rather, “je le sais” can feel very redundant.

In french grammar, there is a notion of “direct object” and “indirect object” that will complement the subject+verb and they can often be dropped from the sentence in shortened, more idiomatic forms.

In “utiliser au micro-ondes”, “au” is a sort of shortened “dans le” (which, again, would not sound very good in French), so it already is the “object” and a “fuller” sentence would not sound as smooth and natural.

Utiliser does not take an indirect complement, so there is no preposition that is particularly associated with it. The following complement is a complément circonstanciel, not a complément d’objet indirect.

Utiliser normally takes a direct complement. Here, it is implicit: the direct complement is the object that the warning is on. The English version uses the same construction: “microwaving” could be replaced by “using in the microwave”.

The construction au/à l’/à la/aux + noun is used for many kinds of tools:

• frire à la poêle (fry in a pan), griller au four (roast in the oven), réchauffer au micro-ondes (warm up in the microwave), …
• couper aux ciseaux (cut with scissors), trancher à la hache (cleave with an axe), …
• écrire au crayon, write with a pencil), …
• à la main (“by hand”), “à la machine” (using some kind of machine), …

A literal translation of “in a microwave” would be “?dans un micro-ondes“, but it doesn’t quite have the right meaning. It implies that the object is placed inside the microwave but not that it’s used for cooking. The preposition dans would only be used to refer to the physical location of the object, not for its purpose (“Où est mon déjeuner ? Ah, il est dans le micro-ondes, j’ai oublié de le sortir.” = “Where’s my lunch? Oh, it’s in the microwave, I forgot to take it out.”).

“À un micro-ondes” didn’t have the right meaning either. You can’t use the indefinite article here because that would refer to one specific, but not yet specified object (“Y a-t-il un micro-ondes dans votre cuisine ?” = “Is there a microwave in your kitchen?”).

Articles and preposition vary a lot between languages and you can’t expect simple translations like “à always corresponds to this preposition” or “if there’s a definite article in one language then the other language will also use one.

As for the noun micro-onde itself, it has two meanings, like “microwave” in English. It’s a term in physics to designate a type of waves, and it’s also a type of oven that uses this kind of waves. The noun onde is feminine, and so is micro-onde in the physics sense since adding a prefix doesn’t change the gender. Micro-onde as the kitchen appliance is masculine because it’s short for un four à micro-ondes.