No, TikTak is a global optimizer in its own right, you wouldn’t use it to polish anything off. The first step in the process is to compute your objective function at a large number of Sobol points! If you have 19 variables, you’d probably want at least 100 starting points I’d guess (I would have said 1000 but no way with 1hr per evaluation).
Given what you’ve said about your setup, I guess box constrained local is probably alright. However, I’m still wondering how feasible it is given that you have 19 variables. How many iterations do you expect it should take to reach an optimum? Even with a crude tolerance, I can’t imagine it being less than several hundred.