Define working days without affecting the calendar

My team travels for business frequently and we need to keep track of the weekends they have traveled on so everyone can get their days in lieu. I used the NETWORKINGDAYS formula and it looked fine. The problem is our weekends are Friday-Saturday instead of the regular Saturday-Sunday. If I enable dependencies to configure the non-working days then the sheet does not allow me to input the start or finish date on a non-working day (sometimes we start or end the travels on a weekend). Is there a way I can configure the weekend days without affecting the entire calendar?

Thanks in advance.