There is nothing wrong with marrying someone who had cancer then recovered; in fact there is nothing wrong with marrying a person who has cancer, so long as the woman agrees to that.
There are many people whom Allah tests with sickness in childhood, then He heals them and blesses them, so a proposal should not be rejected because of that, so long as the person is a righteous Muslim. The Prophet (blessings and peace of Allah be upon him) said: If there comes to you one whose religious commitment and attitude pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption. Narrated by at-Tirmidhi (1084) from the hadeeth of Abu Hurayrah; classed as hasan by al-Albaani in Saheeh at-Tirmidhi.
If the suitor is acceptable in terms of religious commitment and character, and Allah has healed him of this sickness, and his condition is stable according to the testimony of the doctors, then he should not be rejected.
Based on that, try to convince your parents of it. Then if they insist on their attitude, be patient, and accept it and try to find excuses for them, because they are only seeking your happiness and well-being.
We ask Allah to guide you and help you.
And Allah knows best.
Reproduced from Islam QA