Well one must consider that the health of Cavour was not great and the man basically united Italy single handely so was under a little stress.
In any case we can image that the Pod is the presence of his doctor during his last case of malaria so no use of bleeding as cure.
The biggest change that come in mind will be in foreign policy:
- The third war of independece (the southern front of the Austro-Prussian war of 1866) will play a little differently. If the man is still prime minister (a think almost certain) the preparation for the conflict will be more efficient as La Marmora will be no Prime Minister so he will not leave the place just before the war for commanding the army and frankly Cavour will rein both him and Cialdini so their rivalry will not cause the confusion on the conduction of the war (for not talking about the King coming to the front adding some problem). It will not change much on the end but the better performance will be good for Italy self esteem as the war will be a more clear victory and the Iron crow and Veneto will be given directely to Italy without the meddling of Nappy III, the real only change that i can see is Trentino being gained as it was occuppied by Garibaldi troops and the italian plan was to make the aquisition a fait accomplit.
- Aceh, there were an attempt to make it an Italian protectorate but the interest ended when Bixio who was sent there for a scounting mission died and another was done on Papua Guinea but at the time the goverment was not really interested. Cavour was very favorable at the creation of coonies so more support is a given.
- France, Cavour (as great part of the original piedmontese enstablishment) was very favorable to an alliance with France but the 'Roman Question' blocked any attempt from both parts to reach an agreement. I doubt that even Cavour can have the solution at this problem.
- General diplomatic isolation of Italy: frankly i doubt that the just born Kingdom of Italy with Cavour at the helm will be diplomatically isolated as OTL and if he found any occasion to attach Italy to another power he will use it.
The easiest POD is that Cavour would not be infected with malaria. Since when he died he was just 51 years old giving him at least another 15 years would not be asking too much.
The biggest gifts that Cavour would bring to the new kingdom of Italy (same as he brought to his native land of Piedmont-Sardinia) would be an international vision, an outstanding capacity for holding in check the king (and it was very much needed, trust me) and his outstanding capacity to navigate the shoals of parliament (as he demonstrated since the beginning when he built up a strong alliance with the moderate left of Urbano Rattazzi, voiding the attempt sponsored by the king and the prime minister D'Azeglio to engineer a turn to the right).
His leadership would be even more useful to drive the integration of the different (very different) parts of Italy which had applied for annexation or had been annexed tout-court in 1859-60. I am not sure if even Cavour would have been enough to make a full success, but at least he would have assured more stability and would have managed to oppose the alliance between the reactionary Piedmontese right (known as the Camarilla) and the equally reactionary landowners from southern Italy.
It goes without saying that Cavour would have continued his policy of industrialization and infrastructure building (chiefly the railways).
Internationally he would not be necessarily tied to France: the fact that in the 1850s he had by necessity played the French card would not have tied up his hands in the 1860s. IMHO the behavior of Nappy during the war of 1859 and immediately after (the unilateral armistice with Austria, the French clumsy attempt to dominate Italian politics, the support provided to the pope and the ouvertures to Austria in the early 1860s) were more than enough in themselves to be considered full payment for the French support that Cavour had masterfully engineered in the second half of the 1850s. However he was politician enough to know that the French alliance could be openly ditched only when a better one was ready to be formed: Austria was not a possibility, Russia the same, Prussia was still a glimmer on the horizon and the Great Britain of Disraeli (with all the sympathy of Cavour for that nation) was not an alliance on which the newly born kingdom could rely. However the importance of a surviving Cavour was also that he was a known player in Europe, and that his words were more likely to be heard than those of any other Italian prime minister of the 19th century. It would be interesting to see how the approach to the next war with Austria would be played (and another war with Austria was going to come: the situation both in Germany and in Italy was still too fluid for it to be avoided). It would be interesting to see how the relation between Bismarck and Cavour would play out: it is difficult that they would like each other on a personal basis since there could not be two more different personalities. Still both of them were very intelligent men, both of them clearly knew where they were going and how and both of them were more than capable to juggle a lot of eggs in the air without breaking a single one. It would be very good if Cavour would manage to get the right cues from the war of Schleswig-Holstein and from von Roon's reforms of the army: I don't expect that Italy would become a junior Prussia, but it is quite possible that the most rigid and ineffectual cronies of the king in the military might get sidelined (I'm thinking of La Marmora and Persano for example) in favour of new blood.
It's also a given that Italian policies toward the pope would be more assured: the outcome would not be different given the political scenario but at least there would not be a feeling that policies were always made on the spur of the moment.
The biggest question of all, however, is about the south: would Cavour recognize the need for a true land reform, embrace it and force it through parliament against the opposition of the right?
So basically what you're saying is that the man's footprint on history had been completed by the time of his death. Good for him.
What about his conflicts with Garibaldi? Couldn't that escalate into a serious problem with Cavour living?
When Cavour died his footprint in history was no more than 50% done: when the kingdom was proclaimed he said "Italy is made, now we have to make Italians"; his last words on his deathbed were "Free Church in a Free Nation".
Both of them are still quite true even today, but they also demonstrate that Cavour knew his work was very far from complete.
The legend of the hate between Garibaldi and Cavour has been very popular, but this does not make it true. Cavour considered Garibaldi a useful tool, and used him in 1859 and 1860 (don't tell me anyone believes Garibaldi could muster 1,000 men on the quays near Genoa, put them and all their supplies on ship and sail to Sicily without Cavour being informed and authorizing it). He would use again him in the 1860s if the occasion arises but would not let him go on haring on his own (a TTL Aspromonte or equivalent would end up in the same way). Garibaldi was quite pissed off by the French gaining Nice, where he was born, but was more of a gut reaction than a long-lasting grudge. In the end Garibaldi was aware that without Cavour there would not have been any unification.
