This phrase seems to have been taken out of context and given a different focus or nuance, at least in popular culture. Literary people (scholars and so forth) may immediately know the difference.

What are your thoughts and how would you translate it? Has Shakespeare already been translated?

Shall in these confines with a monarch's voice
Cry 'Havoc,' and let slip the dogs of war …

Tabhair/Tabhairigí/Tabhairimis rabhadh “Ródaigh” agus leig/leigigí/leigimis na árchoin.

I think it tends to mean "raise the alarm" idiomatically in the modern day, though obviously the intent here is a shout to indicate raiding should begin.

As a literal translation, maybe "scrois" a scairteadh, but I don't know if that does convey the idiomatic meaning very well.

My preference would be something like "ionsaíg/ionsaígí" a scairteadh

I see. I think at the IGTF we used one or the other words you mention there, but somehow the English word "havoc" was kept in the final version and the guy tattooed it on himself. Something like "Scread 'Havoc' . . ." I cringed and still cringe at that one.