The Investarms made cap locks will fit in the flint lock mortise.
Investarms cap lock barrels geometry will fit the lock, with-in your question, IF the barrel is made for the stock.
A Hawken is a Hawken, a Great Plains is that,
T/C and Investarms are not a direct swap/drop-in fit!
It can be done, but there are modifications that may need to be made. Geometry is close, It's the barrel fit to the stock that's issue.
* The hook/tang of Investarms vs T/C are a little different needing file work to be compatible.
* Position of and thickness of the front wedge vs the barrels under lug,,
* The breech overhang of the lock plate is different.
All that said, any modification will void all warranty.
Point is, Yes, folks have been swapping parts out for decades, but it's not always plug-n-play.
If yer handy, check the archives of other section of this forum that tend more towards your questions of modification or building.