My solar G-7400 has lasted me a while too... I think the batteries needed replacing in about 2010 but it has been going strong since then.
Esslinger has a video on how to replace the rechargeable batteries in some of these G-Shock watches. It's not that difficult if you've got a few basic jewler's tools, mostly the screwdrivers. Fine pointed tweezers including plastic, non-conductive ones help. I don't have the non-conductive but have used round toothpicks (flat ones break and splinter too easily). I do recommend a magnifier that you can put on your head; dirt cheap at Harbor Freight if you're in the USA. Doesn't have to be an expensive one. I've never used finger cots or nitrile gloves, but I am very cognizant about dust motes. Inside these watches, unless you're completely removing the movement exposing the crystal and dial to dust, it's not that critical, not nearly what it is with mechanical movements. The module in your G-7400 should be a 2910 and it uses a CTL1616 rechargeable battery (this is NOT
the common Lithium CR1616 coin cell). Although this Esslinger video doesn't cover your G-Shock specifically, the basics of how to go about it are essentially the same
. Pay attention to the springs and resetting the movement! It's a little more than a standard quartz watch, but not much, and dealing with removing the case back is easier as it's held on with small screws. Google can probably get you a bit more information about what yours looks like with the back off. Using silicone "grease" on the gasket isn't that important either. It's used on screw-down back gaskets as the rim of the back is rotating against the gasket and if it doesn't have some lubricity, it will tear it up. The pressure of the back against the gasket will keep it sealed, and with the backs on these the water pressure only increases that pressure.https://www.youtube.com/watch?v=R6JbrVDqR7w
If you don't want to do it yourself, a full-service jeweler with a real watchmaker in house and not just a band and battery changer should be able to do it for a reasonable cost (ask up front). The rechargeable battery is more expensive than a Silver Oxide or Lithium. I do not recommend ever taking any quartz watch of any kind that cost more than $10 brand new to a mall watch kiosk. They destroy more watches than you could possibly imagine and you're playing roulette with the knowledge and skill of the person manning the booth, or their lack thereof. The overwhelming huge majority of them don't have the proper tools for removing and replacing screw-down and snap-on case backs. I cringe every time I walk by one where the guy is fumbling around with replacing someone's watch battery. A Casio G-Shock back is held on with small screws which is inherently easier to deal with than screw-down backs that require a case wrench or snap-on backs that are best opened with a case knife and best and very easily closed back up with a back press (to keep from breaking the crystal).
I've done plenty of watch batteries myself, including the 10-year Lithium cells in the older Seiko 8F32 series perpetual movements made around 2000, which is anything but straightforward and can easily destroy the paper thin circuit board under the large coin cell if not performed correctly. I've got two 8F32 and an 8F56 and have replaced the batteries in them a couple times. Doing this kind of thing requires a bit of patience, but it's not brain surgery.