Electrum wallet on two different OS (Win7 + Win10)

Hello

Im thinking about installing Electrum wallet and use it to confirm BTC transactions - e.g. instal one wallet on my old computer which is NOT and will NOT ever more by connected to the internet. Thats the "main wallet/transaction signing". And then install the "watching only" wallet on my normal/current PC that is connected to the internet.

I assume you all are common with this setup...? My question is, will it work if both computers have different operating systems installed? The offline computer with the signing wallet has windows 7 (64bit) and my online computer ("watching only wallet") has windows 10 (64 bit) operating system... This setup can work right? It doesnt matter that each computer has different OS installed?

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Correct?