Single word for "I take no pleasure in this" or "I know this seems over the top, but it must be done"
Solution 1:
I presume you've already rejected necessary evil (which isn't a single word), although that does fit the bill nicely.
How about expedient?
helpful or useful in a particular situation, but sometimes not morally acceptable
It might be expedient not to pay him until the work is finished.
The management has taken a series of expedient measures to improve the company's financial situation.
[Cambridge]