He cannot shave his head or cut his hair during ‘umrah because his head is very sensitive; what should he do?

Shaving the head or cutting the hair is
one of the obligatory parts of ‘umrah for men; a man cannot exit ihram
unless he does it. If a person omits one of the obligatory parts of ‘umrah,
he must do it if there is still enough time and he is able to do it. If he
is not able to do it or he misses the time for it, then if he had an excuse
there is no sin on him, and he has to offer the fidyah. If he did not have
any excuse, then he has sinned and he has to repent and offer the fidyah.
The fidyah is a sheep that is fit to be offered as an udhiyah (sacrifice),
or one seventh of a camel or one seventh of a cow, which is to be
slaughtered in Makkah and the meat distributed to the poor of the Haram; he
should not eat any of it. 

The scholars of the Standing Committee
said:

If a person omits any of the obligatory
parts of Hajj or ‘Umrah, he must offer a sacrifice. The sacrifice may be one
seventh of a camel, one seventh of a cow or a sheep that is fit to be
offered as an udhiyah (sacrifice). It is to be slaughtered in Makkah and the
meat distributed to the poor of the Haram.

End quote from Fataawa al-Lajnah
(11/342). 

Shaykh Ibn ‘Uthaymeen was asked about a
man who exited ihram for ‘umrah after circumambulating the Ka‘bah (tawaaf)
and going between as-Safa and al-Marwah (sa‘i), and he did not shave his
head or cut his hair, then he entered ihram for Hajj. What does he have to
do? 

He replied: 

What appears to be the case is that his
tamattu‘ Hajj is not invalidated and is still valid, but he has to offer a
fidyah (ransom) for failing to shave his head or cut his hair, based on the
well-known view among the fuqaha’ that the one who omits an obligatory part
of the rituals must offer a fidyah for that.

End quote from Liqa’ al-Baab al-Maftooh
(5/4). This applies if he has some hair on his head that he can pass the
razor over and shave it, as he mentioned in the question that he had shaved
it. 

But if he went to ‘umrah having already
shaved his head just prior to that, and there was nothing left on his head
to be shaved, then he does not have to shave his head or offer a fidyah;
rather when he finished his sa‘i his ihram ended, and he does not have to do
anything further. 

See the answer to question no.
95439 

For more information, see the answer to
question no.
82077

And Allah knows best.