I've made hot sauce for my family using the following ingredients:
And I would like to try canning it. What can I use instead of vinegar to preserve it. I really don’t like vinegar in my hot sauce at all.
With just those four ingredients (plus maybe some seasonings), your hot sauce will be a "low-acid food" which means that to be shelf-stable, it needs to be canned at 240F/115C. This means that you will need to use pressure canning to seal it (pictoral guide). If properly pressure canned, it should be shelf-stable for months to years.
This has two drawbacks for you: first, it requires getting a pressure canner (or using a pressure cooker and really small batches). Second, it does mean that you're going to be cooking the hot sauce at 240F, which may lead to it being more "cooked" than you necessarily want it to be. If you have a pressure cooker around, I suggest trying that with one jar and seeing how it tastes.