I picked up one of the wax candles this morning at my local Goodwill outlet store. I read your post earlier in the day and just happened to see a 10 cm (~3.8”) tall candle like the one shown in the second link. It was only 75 cents so I figured it might be something worth trying. It’s nice when lit. Certainly worth what I paid for it.
If you are not going to use it frequently where having the remote control is nice, I’d suggest buying the set without it. If you read the reviews below the offering, the first review says the remote control was defective. Not a good sign for a brand new item. A 3 candle set w/o remote is as little as $6.55 postpaid Candles for sale | eBay
Seems like it is off season for a Halloween item. I can see that a mod for this would be to make it work on a single 18650 li-ion battery. Most LED lights that run on 4.5V AA or AAA batteries will also run on li-ion batteries and for an extra $1.75 I could add a remote control to the light housed where the existing AAA batteries are located or simply wire it to a 4.5V DC wall converter.
As to the other set of lights you linked (rechargeable tea lights). I wouldn’t buy them. Don’t expect anything more than a regular cheap tea light and if you buy 10 of the regular tea lights at a time they are about 55 cents each. I’m not a fan of lights that run on button cell batteries, even rechargeable button cells. Those tea lights are powered by a single LIR2032 button cell. The capacity is 40 mAh. I know because I bought a couple of $3 chip-on-board, USB rechargeable, LED bike tail lights recently. They are bright and well worth the $3 but they are throw-away lights when the Li-ion battery goes bad. I took them apart to see what was in the light. The power source is one LIR2032 battery. A replacement battery costs $1.85 but all are rated 40 mAh. Obviously it doesn’t make sense to replace the battery on a $3 light when it finally dies. However it should be good for a couple of years and about 500 recharges.