Yes. It means "I didn't want to sign the contract, but I signed it anyway."
The word should be "reluctance." If that is a quotation, there is a transcription error.
"Reluctance" is a noun. "He showed reluctance, but he signed the contract."
"Reluctant" is a verb. "He was reluctant, but he signed the contract."
"Reluctantly" is an adverb. "He reluctantly signed the contract."
Here are some examples of the use of the word "reluctance:"
"The healthcare industry has a reluctance to adopt new techology."
"Some children have a reluctance to eating eggs."
Here is another example of a word that has a noun, an adjective, and an adverb form:
"A dog shows happiness by wagging its tail."
"A happy dog wags its tail."
"The dog wagged its tail happily."
"Relu