Praise be to Allah.
The basic principle with regard to the udhiyah is that it is Sunnah and one of the visible symbols of Islam, which is strongly encouraged. In fact some of the scholars are of the view that it is obligatory for the one who can afford it. For more information, please see the answer to question no. 36432.
Once it is established that the udhiyah is Sunnah, if a person intends to offer an udhiyah then cancels that intention, there is no blame on him for changing his mind, unless he had specified the animal that he was going to slaughter by saying “This is an udhiyah” or words to that effect, which would earmark it as an udhiyah. In that case he has to slaughter it, and it is not permissible for him to change his mind, because it ceased to be his property when he specified it as an udhiyah.
If he bought it with the intention of offering an udhiyah but he did not specify it as such by saying “This is an udhiyah”, then there is a difference of scholarly opinion as to whether he must slaughter it or not. The correct view is that he does not have to do so, which is similar to the case if he intended to designate his house as a waqf (Islamic endowment) then changed his mind; there is no blame on him. The same applies in the case of udhiyah. See al-Mughni (9/353); al-Majmoo‘ (8/402); ash-Sharh al-Mumti‘ (7/466)
As you had not yet bought any animal to offer as an udhiyah, let alone designate it as such, then you are not obliged to offer an udhiyah on the basis of a mere intention.
It is not essential that a mahram should choose the udhiyah and slaughter it on your behalf; rather if you appoint a trustworthy person to do that, or a charitable organisation, then that would be possible and you would attain the reward thereby, in sha Allah.
And Allah knows best.