Is it permissible to retract the intention of sacrifice on the third day of Hajj due to the difficulty of the sacrificer selecting the animal and directly slaughtering it, and the absence of a mahram to assist her in this?

The Udhiyah (definition) (sacrificial animal) is a confirmed Sunnah (definition). Therefore, whoever intended to offer an Udhiyah and then changed their mind is not blameworthy, unless they designated the Udhiyah by saying: "This is an Udhiyah," in which case they are obligated to slaughter it. However, if they bought it with the intention of Udhiyah but did not designate it, the correct view is that they are not obligated to slaughter it. Since the questioner has neither bought nor designated an Udhiyah, she is not obligated by mere intention. It is permissible to appoint someone to perform the Udhiyah on her behalf.