I will expand if you want.
Going around second hand shops, flea markets and the like I was seeing DS lites go for next to nothing. It has been a while since I last looked and I was not stateside when I did but I can't imagine it changes much, even pumped prices like Amazon and ebay seem to be sitting at around $40-45 USD. With this in mind it would be cheaper to score one in such a place than buying the collection of chemicals you would use to finish this. If you are buying some kind of disposable products to do it in and definitely if you are buying a replacement top screen on top of all this.
If you are buying big boy cleaning chemicals they can have nasty effects on plastic. The DS shells use a common type of plastic called ABS. It is dissolved by acetone (used in some nail polish removers, in chemistry in school you will probably know it as the chemical that when spilled on your hand it made your hand cold), and another called MEK/Butanone which is commonly found in cleaning solutions. It is also mixed with polycarbonate it seems which does not help matters either
Even for all the effort of dismantling a DS (
https://www.ifixit.com/Guide/Nintendo+DS+Lite+Motherboard+Replacement/4784 ) though the board itself could have been contaminated with rat urine. It need not have been soaking in it either as it can evaporate within the box, get in the cracks and then condense again. It is unpleasant stuff for electronics and corrosive enough to note in this. It might work now but if it is there it could sit there eating away at a part of the board without you seeing, or indeed under a chip (I looked at the link and there are no BGA chips on that like I thought there might be, though still small chips it could sit under and wreak havoc for). I can't say it will definitely fail in the near future but if it dies in two weeks I would not be in the least bit surprised.
You can get it done (you will want to neutralise it, wash it and then dry it, none of that is especially easy with basic household equipment). I then said about the times I have done it, however the only reason I did was because it was worth the time, tools and consumables to do it. I would not even say it is a good learning experience.
In all this do believe me when I say I am one for putting in serious effort to fix things, here is a thread I made a while back for a replacement fat ds shell I did for one of mine
https://gbatemp.net/threads/ds-original-phat-replacement-case-review-56k-no.364632/