Given time and equipment, yes. The lightsabers used by the Inquisitorius are mass produced to a standard design, so it's proof that the creation of lightsabers in canon are not limited to only trained Force users - anyone can build one given the right tools.
If done the traditional way, however, then it's not likely. The traditional approach of building one by hand is a highly complex task, requiring one to align the kyber crystal's matrix perfectly with the internal components to prevent it from blowing up, let alone work. In other words, lightsaber construction by any method requires precision at the molecular level.
By the traditional method of constructing by hand, this can only be done by one sufficiently trained in the Force to sense the matrix structure and align it precisely. This is the reason why Vader commented that, with the successful constructing of his own lightsaber, Luke's training is now complete - he has progressed far enough to be a powerful apprentice of the Sith.
As such, for Chirrut to build a lightsaber by hand, he must first be a Force-sensitive. Whether he is one is highly debated, as shown here https://www.starwarsnewsnet.com/2016/11/is-donnie-yens-rogue-one-character-chirrut-imwe-force-sensitive-or-not.html The debate is inconclusive but generally leaning towards a no. Based on this, Chirrut is unlikely to be capable of building a lightsaber by hand.
Assuming Chirrut is indeed Force-sensitive, then he can definitely build a lightsaber, given enough time to train to the level of proficiency in the Force needed to build one. The Clone Wars series has shown that trained younglings are capable of constructing one within seconds. It's the training that takes possibly years (he's no Skywalker).
Of course, all is as the Force wills it. He could even construct from the crystal by hand a handheld Death Star pistol capable of assassinating the Emperor all the way from Jedha without any Force training or sensitivity if the Force decides it to be so.
