[Grammar] whichever method you choose.. or whichever method that you choose..

[Dinusha]

1.Whichever player scores the highest number of points will be the winner.

2.It will be a difficult operation, whichever method you choose.


in above two sentences,can we use that or which after whichever player and whichever method? like,

1.Whichever player that (which) scores the highest number of points will be the winner.
2.It will be a difficult operation, whichever method that (which) you choose.

 

[tedmc]

I would prefer:

1. The player who scores the highest points will be the winner

2. It will be a difficult operation, whichever method you choose. (which/that is not necessary)

not a teacher