More important than fingering is how you use your fingers. Correct fingering will not help you if something is amiss in the arm and prevents the finger from getting to where it needs to be.
Art Tatum famously played many of his scales and arpeggios with only two or three fingers. The secret to playing these scales is to avoid spreading out the fingers and using the arm to place each finger. Abducting the fingers causes your hand to pull in three directions at the same time and that is where tension and uneven playing comes from. The second thing is to come straight down on each key. You can't do that if another finger is pulling the whole hand in the opposite direction. If you miss a note, chances are it is not because of fingering but there is a pull or static muscle preventing you from getting there with proper alignment.
Like, if I asked you to reach to your left for something but I pulled your right arm preventing you from reaching it. That is what happens in your hand when you stretch the fingers out. Better yet, go participate in a three legged race and notice how a single external pull can wreak havoc on everything.
Because the black keys are higher and there are greater spaces in the blues scale, in/out, up/down and arm and elbow movements are required to get the fingers where they need to be, otherwise your muscles will strain to reach each key and not only does it feel awful but it sounds so, too.
I used to play the C blues scale with my fourth finger on the F# and it was always a struggle until I learned to incrementally raise my wrist (forearm) with each finger so the four could come straight down rather than struggling to reach up out of nowhere. Like walking up stairs, your foot must raise higher than the step so that it can come straight down. If not, you trip up stairs. Now I finger the scale with just my one, two and three. The arm gets each finger where it needs to be.
The greater question is why are you spending time trying to play a blues SCALE? Rare is the artist who just plays the scale as a lick. Instead, discover the notes OF the scale and not just the pattern. Don't strive to be an embellisher, but, be an improvisor. Explore just three notes of the scale at a time. Implement just a few notes at a time as part of your vocabulary rather than six or seven saccharine consecutive notes. Play three notes, change direction for one or two notes, change direction again, skip a note . . . . There are no rules other than the laws of physics.
