Keeping Italy neutral might be harder than it first seems.
1935 Abyssinian Crisis when Italy invades Ethiopia. Heightens the risk of war in the region.
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1936 Italian German Protocol
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7 April 1939 Italian invasion of Albania. That led to deterioration of Greco-Italian diplomatic relations and eventually to war 18 months later.
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13 April 1939, in a panicked response, Britain & France offer security guarantees to Greece & Romania in the event that they should be attacked. It was this agreement that generated the need for Britain to go to the aid of Greece in 1940.
22 May 1939 Italian-German Pact of Steel.
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10 June 1940 Italy declares war on Britain and France. The Med had already been closed to British shipping in May on Admiralty advice due to the likelihood of war with Italy. British Somaliland was invaded 3 Aug 1940, starting the East African Campaign. Egypt was invaded 13 Sept, starting the Western Desert Campaign.
8 Oct 1940 German troops enter Romania and a coup installs a pro-Axis Govt, so replacing a Govt with a neutral stance. This increases the pressure on Greece, opening the prospect of a second front.
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28 Oct 1940 Italy invades Greece. Initial Greek requirement was for weapons & eqpt (that saw the USA prioritise production of 30 F4F-3A for Greece over the USN for example). Britain agreed to send 3 RAF squadrons and send troops to to Crete to allow the release of a division for the main front. Negotiations with a reluctant Metaxis begin over a greater contribution, leading to deployment of British forces on the Greek mainland in early 1941.
6 April 1941 Germany invades Yugoslavia and Greece.
So if Italy persists with its aggressive policy towards Albania in Spring 1939 and Britain & France react as historical with the security agreement for Greece, there is every likelihood that Britain gets drawn into a Med war in late 1940 anyway.
Italy on the other hand needs to do much more than simply remain neutral in a war between Germany and Britain & France. It needs to either not invade Albania in the first place, or stop any further dispute with Greece before it gets out of hand. Given the nature of Greco-Italian relations following the break-up of The Ottoman Empire rRom the early 20th Century I think that is a large ask. Issues over running sores like Corfu and the Dodecanese would need to be resolved somehow for that to happen. Otherwise war at some point between the two nations looks inevitable, so raising the prospect of Britain being dragged into it.
The British politics of the time need to be considered. Going to the aid of Greece was also part of Churchill's efforts to influence public, and Govt, opinion in the USA. Plucky Britain, standing alone, going to the aid of another country threatened by the Axis menace.