Is it permissible for a handicapped man, who has one leg shorter than the other, to wear orthopedic shoes during tawaf (circumambulating the Ka'ba) and sa'y (traversing between Safa and Marwa)? Would this obligate him to make compensation? Are the shoelaces considered to be sewn garments?
 

Necessity renders prohibited things permissible

In such a case as mentioned in the question, it is permissible to wear orthopedic shoes with laces because it is a necessity. God the Almighty says:

"He has chosen you and has not placed upon you in the religion any difficulty" (Quran 22:78)
and; "God does not intend to make difficulty for you" (Quran 5:6).

In a hadith reported by 'Amr ibn Yahya al-Mazni through his father, the Prophet (peace and blessings be upon him) said, "Do not harm nor reciprocate harm."

The inquirer for whom it is necessary to wear orthopedic shoes during Hajj, must make compensation by doing one of the following:
• Fast three consecutive days;
• feed six needy persons or give out the value of a meal to each person;
• slaughter a sheep and distribute its meat among the poor, which is analogous (Qiyas) to the compensation made by a person who covers his head during Hajj because of an illness or any harm that might befall him.
God the Almighty says:
"And whoever among you is ill or has an ailment of the head [making shaving necessary must offer] a ransom of fasting [three days] or charity or sacrifice" (Quran 2:196).

And God the Almighty knows best