I want to remove, if possible, the includes of both
There is no simple obvious way to do it (as others have explained it very well).
However these headers should be seen as being part of the language (really!), so you can let them in your own headers without any problem, nobody will ever complain.
If your concern is compilation speed, I encourage you to use pre-compiled header instead and put these std headers in it (among other things). It will significantly increase your compilation speed.
Sorry the for the "real winner is the one who avoid the fight" kind of answer.