FINAL EDIT:

They neighbor saw our note at called me at like 4am. She was super apologetic about the ordeal and I returned her cat to her, along with some cat food and a small bag of litter we bought from a nearby convenience store, since we weren't sure when she'd come back. We wanted to make sure the cat was well looked after til she got home. Again she was super apologetic and as a form of thanks she gave is several mikan. I didn't want them, but I accepted them graciously. I like to think we made a great first proper impression with our neighbors after this! Thank you everyone, for your input!

original body:

While eating dinner my wife and I (both non-Japanese) heard a cat crying loudly in the main hallway. We know it belongs to our next door neighbor , but after ringing the doorbell a few times we figured the owner isn't home. My wife says she thinks it's a young woman.

Being cat-lovers, we stayed in the hallway to keep it company the last two hours. It warmed up to us and its meows have stopped. Thing is, we don't know when its owner will return. I can write kanji, so I'm considering writing a short note with my phone number so the owner will immediately know how to get her cat back.

Thing though is that we're hesitant since we worry the owner may think we're trying to appropriate her cat, or if there's some Japanese law against doing this that we don't know about. Advice appreciated!

EDIT:

We decided to print the note out instead:

お宅の猫ちゃんが外に出てしまい、大きな声で鳴いていました。僕たちは2時間ほど一緒にいましたが、いつお戻りになるか分からなかったため、寒さから守るために猫ちゃんをお家の中に入れました。

お戻りの際は、[電話番号] までお電話いただくか、どうぞ玄関のインターホンを押してくださいね！