Hi Miro,
in ORE we work around these issues by a) interpolating fixings backward flat between simulation dates and b) moving exercise dates effectively to the next simulation date. If you are interested in the details you can look at
a) https://github.com/OpenSourceRisk/Engine/blob/master/OREAnalytics/orea/simulation/fixingmanager.cpp
b) https://github.com/OpenSourceRisk/Engine/blob/master/OREData/ored/portfolio/optionwrapper.cpp
Of course this method introduces a bias in both cases, and the simulation grid has to be fine enough to control the resulting error. In the context of exposure simulation using regression techniques (a.k.a. American Monte Carlo) which you will probably resort to for callable exotics exposure simulation anyway, interpolation using a Brownian Bridge seems to be the most straightforward approach. However we do not provide our AMC engine as part of the open source libraries.
Best Regards
Peter