"guns-a-blazing" is just saying "guns blazing" with a heavy and old fashioned Tennessee accent. Take this scene from Sargent York for example... https://youtu.be/N7lzNAj_hcY?t=3675 This Tennessee accent adds "a" to the front of many words. "was-a-figurin" "ain't nobody-a-holdin ya" "Nate was-a-thinkin" "I'm-a-askin' you for the job" "I was-a-buyin' that land just to spite you"

It originated from "guns all blazing", but it's idiomatic meaning is a little different. When you say 'guns a-blazing' you are injecting a little humour (rightly or wrongly) or sarcasm into a situation where guns are being fired almost comicly in a repeated,noisy, and somewhat haphazard (not accurate) fashion - Similar to a western movie where a gunslinger comes out and fires repeatedly and noisily at someone in the street. If you said 'guns all blazing' there is no obvious injection of humor. So while 'guns a-blazing' has it's origins in 'guns all blazing' the expressions say different things.