Is Psalm 63 about "both Christ and David"? The final verse of the Psalm says...
"But the king shall rejoice in God; everyone who swears by Him shall glory" (Psa 63:11)
Now, which "king" is this Psalm about? The King over all, Jesus Christ! And this Psalm has absolutely NO application to David, because men were only to swear by God's name.
"You shall fear the Lord your GOD, and serve Him, and shall SWEAR BY HIS NAME". (Deut 6:13)
So here we see that David merely a mouthpiece / secretary of the Holy Spirit prophesying about Christ. This Psalm in NO way applies to David, since men were forbidden from swearing in the name of men.