Yes, sometimes Sprint Triathlons are called Tin Man Triathlons but this title goes back, way back to the original Tin Man.
My wife is a walker and a runner and even though I have competed in many more races than she, can tell a fartlek from a plain old fart, and have run in excess of 10,000 life time miles while she is still working on her 2nd grand, she nevertheless has some good ideas when it comes to the sport. She walks a lot before, after and sometimes in the middle of a running workout.
I am not a walker. I will take one of my sons bikes or one of their scooters 200 yards to the corner to mail a letter rather than walk.
Today, after running only 5 times in the last 6+ weeks, I ran an entire 32 minutes without stopping. This was huge for me, since my typical run has been only 16-24 minutes. And why is this noteworthy? I began with a 4 to 5 minute walk. I generally start with a 20-30 foot walk so this was a virtual walking marathon for me before I ran.
When I broke from the walk into a slow jog, my immediate thought was the transition felt normal and relaxed. My next thought was my left upper hamstring isn't hurting or pulling (it has off and more ON since December). In fact in the next 32 minutes it didn't hurt at all. Remember Dorothy's Tin Man in The Wizard of Oz? At first it's just a soft, almost silent groan that emanates from his mouth. The oil can then is applied to his jaws, crooks of his elbows, knees, etc and then he is able to move freely. Walking for several minutes allowed me to move naturally and freely too.
One of running and walking's unpopular cousins is called stretching and I still am an undisciplined stretcher. I would always quip when others encouraged me to stretch before a run, "have you ever seen a race horse stretch?" What race horses do before their race is walk-walk-walk as their warm-up before the slow trot to ready their muscles for the strain ahead.
So leave it to Secretariat, California Chrome and the Tin Man to remind us of that old cliche, "you gotta walk before you can run." It works for me and my guess is that it will probably work for you too.
