I have often heard that the easiest way to guess a woman's age is to look at her hands. I find that keeping my hands looking nice is a constant battle these days. I think I spend more time on my short, natural-looking nails than I ever did when they were long and I changed my polish color just for the evening.
I do not think there is any substitute for using hand cream every chance you get, if you want your hands to look younger. I know we have had that discussion here before, and if you prefer not to use the cream then you will have to accept the limitation that puts on your hands' appearance. I am not trying to be critical here - it's only that our hands take such a beating over our lifetimes, and as we age it really starts to show on us.
Exfoliating is a very good idea. Try for once a week. Follow that with a thick cream or oil and wear gloves overnight, if you want to make your hands softer and smoother. You can use Vaseline, olive or jojoba oil, Aquaphor, or whatever you prefer. I don't think you have to use a special cuticle oil, but if you would enjoy it, go ahead!
You can also use your face peel on your hands, if you use one. Lately I have been finishing up my Peter Thomas Roth peel pad by wiping the tops of my hands with it. This helps with the sun spots that most of us have. Any product with AHA or glycolic acid will work, too.
I can recommend using a glass nail file. I get a smoother edge and far less breakage since I switched. They last forever and all you do is wash it off occasionally. Don't drop it on ceramic tile, however.
For ridges, you could try using a nail buffer. That works for me and my polish looks much better on smooth nails. You may even feel more like going without polish after you buff. This is another thing to do weekly! There are ridge-filling base coats, but I never found one that truly worked for me.
If you can stand it, try wearing gloves when your hands will be in hot water or cleaning agents. I despise them, personally, but this might be the single best thing you could do for your hands.
Make sure you get a balanced diet, especially protein. Women sometimes cut back too far in that category. Some people have success taking biotin supplements, but I've never tried them.
You might try the new polishes that are 3-free, for fewer harmful chemicals. I am using Zoya right now, in the shade Lucy. There are hundreds of nice, light shades out there, but I hesitate to recommend for your skin tone, since I am very cool. Maybe you would like an ivory or sheer nude shade. Zoya's site tells which shades are warm or cool, which is helpful.
Finally, a good base coat and top coat will also help your polish last better.
Spending time on your nails and hands once a week will help you be more proud of them every day. You might even be able to stretch that out for ten days. I think it is time well spent.
In all of this, I assumed that you did not want to go the route of professional treatments. Some women are getting all sorts of laser treatments, peels, and injections to make their hands look younger. That's more than I would want to fool with, or pay for, but to each her own!