Delta is a linear approximation of the change in price due to a small move of the relevant interest rate. Typically a parallel move of the whole interest curve is assumed here. This applies to all kind of fixed income instruments, in particular IRS.
Interest rates can be given as coupon rates (these are the so called par rates, based on prices observable in the market) or zero rates (as a result of a so called bootstrapping process). Both can be used to calculate the price of an instrument so for both types a delta can be calculated. So, if you use zero rates for your linear approximation the result is a zero delta. Same is true for coupon/spot rates.