your own custom model or using a standard one? you can use QuantLib, PyQL, volib, rateslib, arch, dx, ...
If all you're after is deltas (are you, it's not clear), you don't need a "model". In case of sticky strike, delta is just black scholes delta. Correction to black scholes delta for sticky delta can be appoximated well enough from the slope of the risk reversal. Similar correction for sticky local vol can be approximated from the slope of skew.