XPS 9700 charger will charge the machine but won't supply full 130w power required for XPS 9560 The type C Port on your XPS accepts only 100w or less power through charger.  There are other solutions like a TB Dock but are more costly than buying a charger.    So until you get old charger back ,Keep the machine plugged in overnight and do a full charge 
I forgot to take my charger for my 9560. Is it possible to get some charge from a portable power pack or from my cell phone power brick? I won’t be able to get the charger until Friday.
XPS 15 9560 charge