A bit of background
- Knives are always salvageable. While you can nowadays buy a ham knife with this shape:
I read somewhere that originally restaurants started out with concave curved blade chef's knives and demoted them to ham knives when sharpening had removed so much material that they got into this convex shape. So, stop worrying about the state of the metal on the current blade face, that's going to go anyway.
- On having sharp knives
Sharp knives are a pleasure to use. But having them has its costs. And it is not a one-time investment, like painting your walls and having clean walls for the next 5 years, it is an ongoing maintenance process. Like having to vacuum your floor weekly and give it a quick sweep daily to have your floor clean. So, you have to decide if you want it - it is a matter of weighing your frustration with dull knives, and your enthusiasm for knowing how to do it and enjoying your tools, against the cost of creating one more chore. If you were OK with dull knives for 12 years, you may have a revelation once you feel the pleasure of a sharp knife, or you may put it on your "todo when I find the time" list.
What you can do with the knives
So, with that in mind, what you do depends on your future plans. If you want to have always sharp knives, it is good to learn how to care for them yourself (sharpening and stropping). In the long term, it will save you money and the logistics will be much easier. In the short term, it will be time-consuming and frustrating, because you need quite some exercise before you can do it well. In that case, be sure to keep these knives - it's best to have cheap items for learning, instead of getting good ones and still having them cut badly because of the bad sharpening jobs you will create at the beginning.
If you want to have always sharp knives, but don't want to spend the time needed to sharpen your own, you could plan to get a set of good knives and send them regularly for sharpening. In that case, you can buy one good knife, have one of the current set sharpened, and compare. Is the current one good enough for you when professionally sharpened? If yes, keep the set and have it sharpened when needed (note that you will still have to learn how to do the between-sharpening-maintenance at your home, but that's much easier than sharpening itself). If the difference to the expensive knives is worth it for you, get those.
And if you think that this desire to sharpen is a one-time thing, but you are not going to grow into a knife aficionado and will probably keep the knives as they are for the next 5 years before thinking of sharpening them again - then both a new knife set and learning how to sharpen are a waste of money or time. Send them away to the professional once, then keep working with them as you want.
If you have the money but not the time, you may also look into getting a ceramic knife or two, the good (and expensive!) ones keep sharper than unmaintained steel (but duller than maintained steel). They are not a silver bullet, because they are also more sensitive than steel, but can be better than your current setup. In that case, keep the old ones too, to have enough knives, and for jobs that are not good for the ceramic.