likelihood of Master's application being rejected due to obsolete GRE and IELTS scores
GRE/IELTS scores are far from the most important part of your application. The faculty reviewing your application are likely to overlook this if the rest of your application is strong.
However, the problem is that the applications may be filtered by computers or administrators before they reach the faculty (e.g., to remove incomplete applications) and they tend to be less forgiving.

A particular concern for you is that your scores will need to be verified at some point before you can register as a student. This requires you to get ETS to send the scores directly to the university. However, as far as I know, ETS will not send expired scores. Thus you will not be able to verify the expired scores and you will not be able register.

As annoying as these tests are, I suggest you re-take them to avoid the possibility of missing out on grad school for a silly reason like this. If you really cannot re-take the tests, you should try your luck, but I suggest that you make it clear on your application that the scores are expired. The worst thing would be for the university to think you have misled them.