If we're going to go for an accurate model, then, we'll need the following conditions:
1 June 1941-7 May 1945 for our timeframe. 1944 was a leapyear so that adds one extra day.
That gives us 1437 days, or 124,156,800 seconds. We'll assume 6 hours per day for sleeping plus 2 hours per day for eating, excreting, and mustache grooming, but zero additional seconds of wasted time due to that SS efficiency. That means he only has 82,771,200 seconds in which to stab. This is where things get tricky.
For 1941, let us assume that he is still fairly out of shape and is suffering from the strain on his arms. We'll equate that to 2 seconds per stab, and 2 stabs per fatality, which gives us a kill ratio of 1 death per 4 seconds. 1941 is responsible for 12,326,400 of the total stab-seconds available, so in 1941 from 1 June to New Year's Eve at midnight, Hitler stabbed 12326400/4 = 3,081,600 people.
After that, he'll be in fairly decent shape as far as his arms go, so we can drop the rate to 1 stab every 1.5 seconds and 1.5 stabs on average for a death. That increases the kill ratio to 1 death per 2.25 seconds. Now, from 1 January 1942 to 7 May 1945 there are 82771200 - 12326400 = 70,444,800 stab-second available. At 1 death per 2.25 seconds, that works out to Hitler stabbing 70444800/2.25 = 31,308,800 people.
The total number of deaths by Hitler-stabbing between 1 June 1941 and 7 May 1945 then works out to be 34,390,400 people, or a little more than three times the actual number of deaths in the Holocaust. By way of comparison, the estimated population of Germany (and annexed territories) in 1939 was approximately 80,600,000 people. For another comparison, the total number of deaths in World War 1 was roughly 16 million.
In conclusion, if Hitler had spent every free moment from June 1941 to VE Day stabbing people in the face, he would have been personally responsible for more than twice as many deaths as World War I.