I also use a dive watch, no back up computer. For recreational, NDL diving, that is more than sufficient.
It's great that you are going through this intellectual exercise. You might think about a couple of things:
1) The dive computer only tracks your depth and time, it does not have any idea what your actual tissue loading is.
2) It then spits out numbers that are theoretical representations of your N2 exposure. Different computers will spit out different numbers, and some numbers (like NDL on the ascent at the end of a dive) have no actual relevance.
3) There is no magic line between a dive that is perfectly safe to surface from, with no possibility of DCS, and one that is not safe. There is a very large 'grey area' where some divers would be fine ascending on some days, and others diving the same profile might suffer DCS. You probably want to avoid this grey area as a new diver, and learn to mitigate any risk you might have on longer, deeper dives, especially repetitive ones. This is best done through greater understanding of the factors in DCS exposure (some of which have nothing to do with your dive) and acting accordingly.
Here's an example of this last bit. If you follow what happens with some dive planning software (a great tool for learning BTW) you will learn that usually, the initial required deco stops, as a diver slips from an agressive NDL dive into a required deco, are shallow. Often an extended stop at 10 feet is the first deco requirement, although some software or computer settings will set the stop at 20 ft. So lets say you are on a dive, your computer stops working, and you are concerned that you might have 'stepped over the line' into some required deco. You could simply do your normal safety stop at 15 feet, then do an additional, longer stop at 10 feet. Or you could do your safety stop at 20 feet for 3 minutes and then proceed to 10ft. How long? As long as you want, maybe 10 minutes if you have the air and time. It's not necessary, but it might make you feel better. Better psychologically about a surfacing without the computer's ok, and better physically, because long shallow stops are known to be very effective at reducing N2 loads in recreational diving.
This long post is really about learning not to be a slave to the computer. It's your dive behavior (and topside behavior as well) that determines your risk for DCS. The more you learn about this, the better equipped you will be to dive safely, and mitigate the risk if you eventually decide to dive deeper, longer dives.