They could actually force the Savoyards. The British controlled 31% of Sardinian trade in 1860 and the French controlled 26%. Losing 57% of the Sardinian foreign trade would have been disastrous for Sardinia-Piedmont whilst losing Sardinian trade would not afford a blimp in both Paris and London. Nonetheless the plan was favored Niutta, Natoli, Peruzzi, Mingheti, De Sanctis, Vegezzi, and Cassinis, the vast majority of the Sardinian cabinet.Neither France nor the UK could in any way force the Savoy to do anything, as both could not intervene.
However it is your timeline, and I don't want to interfere.