May one delay the second washing with the blessing until he goes to Mikveh?
One is to wash with a blessing of Al Netilas Yadayim and recite Asher Yatzar/Elokaiy Neshama right after he goes to the bathroom after washing near his bed, as stated in Halacha 8B. One is not to delay this washing with a blessing until after he immerses in a Mikveh.[1]
If one is a Baal Keri: Even if one is a Baal Keri he is to nevertheless follow the above procedure and wash after using the bathroom, and recite Al Netilas Yadayim and Asher Yatzar. He is not to delay the blessings until after Mikveh.[2] [Regarding Elokaiy Neshama and the remainder of Birchas Hashachar-See Chapter 8 Halacha 9 in Q&A!] Nevertheless there are those that are accustomed not to say any blessings until after they have immersed and purified themselves from their state of Keri.[3] One who follows this custom must proceed to the Mikveh immediately upon awakening and wash with a blessing right after Mikveh.
[1] 6:2-5; Siddur; Shulchan Menachem 1:6; Sefer Hasichos 1944 p. 20
[2] So I received from Harav Yosef Simcha Ginzberg and other Rabbanei Anash; Darkei Chaim Veshalom 9: When the Munkatcher would immerse Tevilas Ezra he would say the blessings of Al Netilas Yadayim and Asher Yatzar beforehand while Elokaiy Neshama he would say in his mind until after he immersed; See also Sefer Hamamarim 5672 Vol. 2 P. 737
[3] Mishmeres Shalom 2:1 and so is the custom of many Chassidim; See Maor Vashmesh Emor regarding not even thinking Torsah beforehand; See Shulchan Melachim [Tevilas Ezra] 20; Based on Ketzos Hashulchan 12 footnote 9 there is no interval actually being done between the washing and the blessing being that the blessing is being said on the second washing.