Your analogy of the surgeon reminded me of what Augustine said in the City of God:
"Now God is in such sort a great worker in great things, that He is
not less in little things,—for these little things are to be measured
not by their own greatness (which does not exist), but by the wisdom
of their Designer; as, in the visible appearance of a man, if one
eyebrow be shaved off, how nearly nothing is taken from the body, but
how much from the beauty!—for that is not constituted by bulk, but by
the proportion and arrangement of the members." (Augustine, City of
God, Part II, Book 11, Ch. 22)
I don't want to say that that's necessarily incorrect, but to some extent it gives the impression that we should accept a little bad with the good, especially when he says "nearly nothing is taken from the body", and I really think that's unnecessary. A better perspective would be that there is not, never was, nor ever will be any single event which is not one of God's good works for which He should be praised.
In order to understand this perspective, it's necessary to understand a very fundamental principle which is taught from Genesis through Revelation, namely, God works good deeds through man's evil actions. Perhaps the clearest example of this is in Genesis when Joseph's brother's sold him into slavery. After being reunited with his brother's, Joseph clearly states:
"You intended to harm me, but God intended it for good to accomplish
what is now being done, the saving of many lives." (Gen. 50:20)
The amount of Scripture that could be cited on this subject is very extensive, so I'll skip to Revelation to find another example.
"The beast and the ten horns you saw will hate the prostitute. They
will bring her to ruin and leave her naked; they will eat her flesh
and burn her with fire. For God has put it into their hearts to
accomplish his purpose by agreeing to hand over to the beast their
royal authority, until God’s words are fulfilled." (Rev. 17:16,17)
It might also be helpful to understand that a thing can be both good and not good at the same time if it is not in the same sense. As long as that final clause is remembered, it is not a violation of the law of noncontradiction. For that reason, an event can be said to be evil because some human being had wicked intentions to do what is wrong, and the same event can be said to be good because God had praise-worthy intentions to further what is good. The entire course of history is the glorious succession of God's good works, one right after the other.
We can admit there's evil in the world, but that's looking at it from the perspective of the guilt which accrues to man. If you look at it from the perspective of the guilt which accrues to God, there's no evil at all. It's also important to note that removing any evil event perpetrated by man would also remove one of God's works and thus diminish the perfection of His plan.
To answer your question: Is belief that everything that happens is God's will inconsistent with Theism?
On the contrary, the only way that Theism can be consistent with the problem of evil is by recognizing that everything that happens is God's will, because only a sovereign God can bring about good through man's evil deeds.