To speed things up, try using a solution of baking soda rather than it's paste. Alternatively you may like to use a solution of warm water mixed with some salt and/or freshly squeezed lemon juice. In both instances, best to leave the rubber portion soaked overnight.
Depending on the material used, whether it's natural rubber or some other thermoplastic elastomers, the results may vary. The smell is probably from the out gassing of volatiles from materials used, and will likely reduce on its own naturally after some time if left alone in the open.
Hope it works out well for you. Cheers!