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I am new to 30k so I have no idea how big of an issue this is since 30k appears to be more re-enacting minded than 40k usually is.
The Blackshield outsider army fluff is interesting enough for me to consider starting an army, but none of their rules (mainly you can deep strike + some semi useful items) do seem that attractive to me. And them not being able to use generic generic rites of war is really restricting especially since a few of them would really fit the theme that I had in mind and would perfectly fit the whole rogue space pirate feel.
Would it be frowned upon to just use the generic legion list, and model them like black shield outsiders ?

I don't believe it's required, but you will find yourself rather restricted with no special characters or units, and very often your units will be outclassed by their equivalents due to the lack of extra special rules.

There's a provision for doing something like that. From "Legion Astartes Special Rules" in the AoD Army List book:

Unlisted Legions: If you are using this army list to represent a Legion which does not yet have its own unique Legiones Astartes rule, you may instead add either the Stubborn or Furious Charge special rule to the standard provisions of this rule in the interim.

I don't mind if you use non-Legion-specific rules, so long as you aren't using other legion rules. (There was a somewhat heated thread on here about representing Blood Angels with World Eaters rules and I'm personally not with that sort of thing).

Agree with above.

Using a specific Legion army but just modelling them like Blackshields is pretty fluffy - Blackshield gotta come from somewhere and maybe this Blackshield force were originally, say, Ultramarines, so still use their organisation and tactics.

Call them Renegade Ultramarines so you don't confuse people with the Blackshield tag.