Sorry, but those tools do not give you direct control of the step size. However, if you are using fminunc, then is there a good reason why you would not just use fmincon? Since fmincon will allow you to place constraints on the problem, why not use a tool that is approperiate for your problem?
Yes, you could write the code yourself, but that would take far more effort than simply using a more appropriate optimizer.
And, yes, you make a statement that the bounds are unknown (which means effectively nothing, since then how will you decide to control the stepsize?) But you can always choose some arbitrary bound on the cost function, which you claim can grow towards infinity.