Day count for non-resident tax returns that include international travel

I work for a Swiss company in NJ and live in NY. The NJ company has me travel to and work in Switzerland on a regular basis. My W2 lists all of my income for NJ and makes no reference to the time spent in Switzerland at the corporate offices. I have no NY W2 income. When I file my NY return I file a NJ non-resident return. As the W2 indicates all of the income as NJ income I file an NJ return for 100% of the income and then file the NY return with the NJ taxes basically offsetting the NY taxes (the rates are very slightly different but they basically offset each other) How will NY consider the days spent in Switzerland? What do NY and NJ do for day count calculations?