Normally, if possible, you should get the correct crown for that model which might end up being also 4mm or not. First and foremost it's the hole in the crown that matters as it'll be connected to a stem and that stem has a certain thread size.
If your watch has both day and date then it'll have two rings. There is a chance that one or both might fit the Omega but I quite doubt it and, again, you should fit original ones for that movement. Also, just because these features aren't working it doesnt mean that you have to change the rings. Maybe the issue is fixable during servicing of the movement.
How reliable was the one servicing the movement ? Normally servicing means that your watch comes back FULLY functioning. Did they tell you WHY the day/date function isn't working ? More so they should have replaced the crown with a genuine one but that one depends on their stocks and a few other things.
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