I don't see how Hawke is even in a position to criticize Merrill; he doesn't know about the plight of the elves, about the culture or trials and tribulations of the Dalish, about the lore of the Eluvians (that Merrill has studied as part of her efforts to construct her own Eluvian). It's that old trope where 'human knows best' even when said human is completely ignorant about said culture.
Of course, Briala's story proves that Merrill was correct about how useful the Eluvians could be to the elves, so this is a moot point. 
Obviously, the Andrastian human who knows nothing about elves except they're servants and laborers who clean his/her cushy mansion (Orana) knows more about elven history, lore, magic, and technology than the Dalish scholar who's been studying these things her whole life.
Funny how Briala's and Solas' Eluvians in TME and DAI vindicate Merrill's view that the Eluvians can be used to help the elven people, but somehow they don't count.
This isn't necessarily about elven culture or lore. Or even the Dalish. It is about one elf: Merrill. Hawke doesn't have to be an elf to see how following blood magic is hurting Merrill and her clan. Is Merrill's life/sanity worth the possibility of an artifact being repaired? Is Merrill's clan? Is Kirkwall?
Nope. Merrill used blood magic on the mirror once, to cleanse the shard of the darkspawn taint that killed Tamlen and Mahariel. Even then, she only used blood magic that one time because Marethari refused to lend magical power to cleanse the shard, and she didn't have access to lyrium at the time.
You could argue that Merrill should have waited to gain access to lyrium or asked other elves, but considering how Marethari poisoned the well by telling other Dalish elves that Merrill was trying to do something dangerous before she could even approach them, and how dangerous it is for apostates to reveal themselves in Kirkwall, one could counter-argue that it would have been more fruitless or dangerous for Merrill to try that way.
Merrill learned how to use blood magic by Audacity without setting it free, and then used blood magic once to cleanse a tainted shard so it was clean and safe again. She then successfully left Audacity where she found it (showing no danger there), and then used regular magic and her own two hands to keep recreating and repairing the mirror for years.
The tool she asks Hawke to bring her after three years is, by all accounts, a simple hand tool that she can use without magic.
Your argument that withholding the Arulin'Holm, a simple woodcarving device, on the grounds that you're trying to discourage her from using blood magic rings hollow, since there's no evidence that she's been using blood magic to repair the mirror after the initial cleanse, and the tool she needs to physically repair the mirror is a physical hand-held tool that doesn't require blood magic.
EDIT: Then again, doesn't Merrill have the blood magic specialization for combat purposes? Any Hawke who brought Merrill along as a companion and let her use blood magic to fight baddies in the name of Hawke making money, but then turned around and says they tried to stop her from restoring the mirror (which she almost never uses blood magic on) in the name of discouraging her from using blood magic on, rings really hollow to me.