I know it's frustrating. I recommend letting it go and not pressuring him to walk either assisted or unassisted. Offer his hand, entice him with something, encourage, but if he won't, just drop it. He will get there. My DS didn't start walking until 15 1/2 - 16 mo but could have, physically, much earlier. He had more fun crawling and didn't yet realize it was faster and more fun to walk. I knew he COULD if he just tried, but I also didn't stress about it, I knew he'd get there on his own time. He stuck with what he knew he could do well, that that is OK, it's not stubbornness or refusal. He just needed to be ready and it was totally fine in the mean time!
Try to relax, and just play and be a safe refuge for him.
ETA: keep in mind that he is a boy - girls tend to do all these things earlier. And try your best to avoid comparing to other kids his age. From my recollection, up to 18 mo is considered normal to start walking.
and your comment about cautious and independent...my DS is a lot like that too. He's pretty cautious, careful, thinks a lot and never just jumps into things, and he's also independent. I think he will be that way for a long time, so I try to remember that is part of who he is.
And to anyone reading - it's NOT delayed! Not at all. Totally in the range of normal. He's not late, he's not behind, not one bit. I have said that my DS walking (and crawling) was on the later end of normal but still VERY normal and not concerning one bit. Try not to think of your sons as being behind at all!