If you have decided to do ‘umrah during this trip of yours, it is not permissible for you to pass the miqaat without entering ihram for the pilgrimage that you have intended to do. So you should form your intention to do ‘umrah, and say: “Labbayk Allahumma ‘umratan (Here I am, O Allah, for ‘umrah).”
If you are coming from Egypt or elsewhere, then the pilot of the plane will usually announce the miqaat, so you can ask them, if they do not do so.
The same applies if you are coming by sea.
What I understood from the answer you refer to is not correct, because what is meant is not that you can delay putting on the ihram garments after entering ihram for ‘umrah and passing the miqaat. Rather what is meant is the opposite of that: you can prepare for ihram by doing ghusl and switching your ordinary clothes for the ihram garments, even if you have not yet reached the miqaat, then when you actually come in line with the miqaat, you have to enter ihram for the pilgrimage that you want to perform (by saying “Labbayka ‘umratan (Here I am for ‘umrah” or “Labbayka Hajjan (Here I am for Hajj)).
If you passed the miqaat without entering ihram for the pilgrimage and putting on the ihram garments, then you must go back to the miqaat and enter ihram from there. If you do not do that, then you have omitted one of the obligatory parts of the pilgrimage, whether it is Hajj or ‘umrah, and you must offer a sacrifice to compensate for that.
There is no reason to delay your ‘umrah until Friday, for there is no special virtue in doing so. Rather what is best in your case is to enter ihram for your pilgrimage from the miqaat stipulated in Islamic teaching, then complete your ‘umrah. Then you will be free to do as you please after that.
And Allah knows best.