The amount of execution time is a simple public parameter of the system.
These schemes require reducing the verification program to a circuit in advance, so its execution time is already fixed by virtue of that translation.
(In practice the existing implementation is not using constant time cryptography; and so it could have timing/cache/EMI side-channels; but this is "just engineering")
There are a myriad of ways to leak timing information from something like this, and to mask them amongst legitimate-seeming computations.
It seems like if you're having to rely on manual program inspection, then you've already lost.