If one’s hands are dirty, must he wash his hands prior to saying a blessing?
Some Poskim rule that one whose hands are dirty [with food, oil or other substance], is obligated to wash his hands prior to saying any blessing, as the law of Mayim Achronim is not limited specifically to Birchas Hamazon. Thus, if in middle of a meal one desires to drink wine or eat a fruit, he is to first wash his hands if they are dirty. Likewise, prior to saying Borei Nefashos or Al Hamichya one is to wash his hands if they are dirty. However, according to those who rule that one is no longer required today to perform Mayim Achronim, there is likewise no requirement to wash dirty hands prior to a blessing, unless one’s is particular to always wash his hands. Practically, if one hands are dirty to the point that one would normally be particular to wash them, then they are to be cleaned prior to reciting a blessing. One may clean them with a towel, or water. If, however, they are not dirty to that point, one is not required to wash them before saying a blessing.
 M”A 181:9; Sefer Chassidim 58 and 853; Zechor Leavraham Mem; P”M 181 A.A. 9 [Is obligation by all blessings]; Kaf Hachaim 158:53; 181:29; Piskeiy Teshuvos 181:2; See Zohar Balak “One who says a blessing with dirty hands is liable for death”
 M”A ibid; Sefer Chassidim ibid
 P”M ibid; Shaar Hatziyon 181:32; See Binyan Shlomo 1:11
 See Admur 181:9 and M”B 181:23
 Admur ibid regarding an Istinis saying a blessing on wine during meal; M”B ibid
 Implication of Admur ibid and M”B ibid who write Kinuach; Piskeiy Teshuvos ibid
 Implication of Admur ibid
Ruling of Admur: From Admur 181:1 and 9 it is implied that washing the hand is not necessary prior to a regular blessing even if in general one is particular to perform Mayim Achronim [Admur ibid constantly writes the term “Birchas Hamazon” when discussing the obligation of Mayim Achronim, hence implying that by other blessings there is no prohibition to recite them with dirty hands] Furthermore, Admur 181:9 limits the ruling of the M”A and Sefer Chassidim ibid specifically to a case of an Istinis.