Take a look at this bag. I have put it into a couple of leatherworking articles because the stitching is typical of the 18th century. The tight, small stitches can only be made with a tapered thread end, a small bristle or needle, and a smaller bladed stabbing awl.
Sometimes a welt matters, and sometimes it doesn't.
In a practical sense a welt will do a couple of things. It will shelter stitching, but it is questionable whether it will protect it. When thread gets wet,and then dries and suffers the mould in the leather around it, it'll rot. period. With a welt, though, it gets less of that exposure because more of it is hidden. IN a modern bag, the greater impact on thread is because of larger holes that are stabbed and waxed thread that does not fill them.
The two best skills my master taught me was how to taper a thread end and use a smaller needle( or bristle) AND how to sharpen and polish my awl so that I could stab a hole in which both sewing threads fit tightly.
The major support against rot was not so much the welt, but the handwax that saturated the thread and burned itself into both thread and leather when a stitch was pulled closed.
The second effect of a welt in a bag is to help prevent the leather from..."grinning"...when the bag is turned inside out. An un-welted seam may finish unevenly turned, or twist and turn along its course resulting in a lot of extra work to force it straight, especially when skived along the edge before assembling ( or closing) to get the bag to even out. Sometimes that happens and sometimes it doesn't.
So, go ahead and welt. Looks macaroni anyway.
Unless you are proficient at COAD ( or handwax) which is made by combining pine pitch, resin and a little oil whatever else you wax your thread with will only go so far in keeping out the rot...HOWEVER...that's usually a long time the way we use bags and such.
Don't be so quick to shy away from artificial sinew, but, before you buy a roll, try to untwist about three inches off the end. You can smear it back together again easily because it just a bunch of nylon slammed together with a lot of wax. The better rolls look like a thin ribbon that is quite fine. It will twist and combine well with either linen of hemp thread. You can get it to look almost imperceptible when as one single ply and make the stitches last a lot longer. The key is to be able to break it into a sinlg strand ( or ply) rather than leave it in bulk.
I usually sew with one ply linen and two plies hemp and maybe one ply artificial sinew if feeling frisky.
Three years ago I came back to rendezvous at Slippery Rock after a brief ( 15 year) trek into cowboy action shooting, and a guy showed up with a pair of shoes I made him twenty years ago. He wanted a replacement pair and I was surprised he wasn't crippled because everything on those shoes was beat into submission except the stitching.
As always, there's a lot of good advice in these threads.
The Still River Cordwainer ( AKA The Capgun Kid