This is an interesting topic.
My position on the matter is that it's not only Hashirama's DNA but any Senju DNA combined with Uchiha DNA is capable of awakening the Rinnegan, so it is not a conditio sine qua non that only Hashirama's cells could be used to awaken the Rinnegan, however, Madara's choice in choosing to use Hashirama Senju's DNA is not a matter of necessity, but a matter of favorable outcome in terms of maximum probability, Madara, who has the most powerful Uchiha DNA would naturally chose the most powerful DNA of the Senjus: Hashirama's, since the combination of the optimal dominant genetic traits of these two bloodline woulds result in the maximum probability of awakening the Rinnegan, if Madara had chosen a less powerful Senju then his chances of awakening the Rinnegan decreases none the less, the mechanistic principle as specified in Manga canon remains, that Senju DNA per se combined with Uchiha DNA is possible in awakening the Rinnegan, but with lower chances of actualizing the desired outcome.
My position on the matter is that it's not only Hashirama's DNA but any Senju DNA combined with Uchiha DNA is capable of awakening the Rinnegan, so it is not a conditio sine qua non that only Hashirama's cells could be used to awaken the Rinnegan, however, Madara's choice in choosing to use Hashirama Senju's DNA is not a matter of necessity, but a matter of favorable outcome in terms of maximum probability, Madara, who has the most powerful Uchiha DNA would naturally chose the most powerful DNA of the Senjus: Hashirama's, since the combination of the optimal dominant genetic traits of these two bloodline woulds result in the maximum probability of awakening the Rinnegan, if Madara had chosen a less powerful Senju then his chances of awakening the Rinnegan decreases none the less, the mechanistic principle as specified in Manga canon remains, that Senju DNA per se combined with Uchiha DNA is possible in awakening the Rinnegan, but with lower chances of actualizing the desired outcome.