(Given that 100 years feels more "neat.)
In my head, I have the idea that other examples of these 99 year leases. Is this accurate?
Additionally, the only knowledge I could dredge to the task was that in Medieval English Law, a year and a day was used in place of a year because it gave a specific date, disallowing the vaguery that "a year" might bring.
I do not know where or how you'd find out the exact rationale for Britain chossing a 99-year lease, but your suggestion that it came as part of a series of other leases with other countries seems to gel with what little I've been able to find. This recent answer of mine goes into more narrative detail, but needless to say the 99-year period may have been chosen to match similar arrangements made with Germany regarding Qingdao and France regarding Guangzhouwan, as the French were demanding exclusive 'rights' to territorial concessions in Guangdong as part of the Guangzhouwan arrangements, cutting off potential expansion of Hong Kong's territory by Britain.