I don’t
know. Obi-wan’s knighting was never described in details. we know we
happened
in Naboo and that he was knighted for killing Maul. That’s it. As far as I
know, these details like who cut his braid were never revealed. We know it happened somewhere between the moment Yoda informs him the Council allowed him to train Anakin and the Theed celebration. If I had to guess, I’d say
it was Yoda who cut it. It was the job of the Grand master to cut the padawan’s
braid during the Knighting Ceremony. Even if Qui-Gon had lived, he wouldn’t be
the one cutting it. If Yoda was unavailable, a member of the Council could do
it for him.