Correct. There aren't any software settings in Nintendont to assist with delay, at least that I know of. It really depends on your TV model, as they handle processing differently, but generally speaking, yes, the HDMI adapters will handle the processing faster than MOST (not all) TV's when it has to upscale the signal from the AV (red/white/yellow) inputs, assuming that's what you're currently using. I've been using one for years and it definitely feels like CRT. But that's also because my TV has a very low input delay, which is the main factor you have to take into account. (Note: Input lag is often different from what is commonly labeled on the manufacturer specifications as "response time"). There's a huge range of delays between makes/models of TV's. This article goes more in depth on what goes into the game 'lag'. You don't really need to understand all of it in depth, though:
We have a guest, Jas "Fizzi" Laferriere (Twitter @Fizzi36, Email: Fizzi36@gmail.com), who put in lots of interesting research into input lag. EDIT: I have written a short follow-up to this article with recommendations about monitors and devices check it out here: Reddit Post Table of Contents...
www.meleeitonme.com
If you haven't already, you'll also want to find out the input lag for your display you're using.
https://displaylag.com/display-database/ &
https://www.rtings.com/monitor/tests/inputs/input-lag both have a lot of displays they've tested and are pretty reliable.
If you can't find it anywhere, feel free to post your TV make/model here and someone could try to help find it possibly
For the HDMI adapters, I suggest going with the Wii2HDMI or any of the same style. There's multiple ones that look almost exactly the same. I've used a few, and the cheapest ones seem to work just as well as the pricier ones - I'm pretty sure they're all made by the same manufacturer.
Here's one on eBay currently for $4 -
https://ebay.to/2JoYOak
Good luck!