Is there any way to eat a tuna wrap from a non-kosher restaurant, if I have full access to see their ingredients and packaging?
Not recommended. What an amazing coincidence that you are asking this question in Adar, when we will read in the Megilla how Achashverosh served a Glatt Kosher party to the jews and they deserved to die for joining in the party. Let us learn the lessons of Purim that not everything that is seemingly Kosher is recommended.
The question is premised on an unlikely scenario. Did they let you into the kitchen and show you the industrial containers of tuna, mayo, oil, salt, pepper? Did you see them remove the wrap from the packaging? Did they microwave it first to soften it? Was the microwave clean? Did they check the lettuce? Did they cut the tomato without using the ham slicer? Was the work surface clean? Was the knife, spoon and fork new or cleaned properly? Was the mixing bowl clean?
If yes to all of the above, well then you basically made the sandwich yourself with your own kosher components. What's the problem?
Perhaps you meant to ask, "may I cut cold kosher food with a clean non-kosher knife?" The answer is: no, you may not, but post-facto it is OK. See Shulchan Aruch Yoreh Deah 121:7 for the right way to do it: by kashering the knife first.
Of course, ask your local rabbi first.