Does an 'Umrah performer incur a sin, blood, or expiation if they bathe but do not apply perfume to their body before assuming Iḥrām due to its unavailability?

Applying perfume to the body before assuming the state of Ihram is recommended but not obligatory. This perfuming of the body is specific to it, as narrated in the Sahihain from Aisha, may Allah be pleased with her, who said: "I used to perfume the Messenger of Allah, peace and blessings be upon him, for his Ihram before he entered it, and for his release from it before he circumambulated the House."

Therefore, not applying perfume to the body before Ihram does not necessitate anything.