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I doubt that will actually save you time. You would need to make the new file, include all of the necessary code for generating the Show Team page, yet modify it so that it works with your single global template. That may take some doing. For example, the way that the user entries are generated by default is by calling the showteam_usergroup_user template once for each user being displayed (at least I would assume so, I haven't checked the code), modifying the user variables to be appropriate for the current user being generated. You would need to find an alternative way to allow multiple user entries to be dynamically generated and code the alternative. You would of course need to modify the global template appropriately, and modify all templates that link to the showteam.php page to reference the new page. Or, if you just replaced the original showteam.php page, it would be overwritten if you update MyBB and it makes a change to that page. You could try to avoid updating that page, but then you won't have the benefit of whatever bug fix or security update that came with that version.

My point is, even if it looks inefficient, usually there's a good reason why a single MyBB page is split across multiple templates. You would probably find your life easier if you worked with the existing framework. What Leefish proposes should be pretty quick to implement if you have a basic knowledge of PHP and SQL, which it sounds like you do.