Right now the closest you'll get is creating "shortcut" applications that launch a game from an R4 which is very doable. I recently confirmed DLDI capable NTR mode homebrew can access storage on original R4 cards. So you could create a launcher that sends a command to a rom manager on the R4 (one that has argv support maybe. Perhaps some special version of Moonshell or something. Not sure if WoodR4 supports this) to start a specific game.
Not even sure the current rom managers for R4 support this. In that case, have fun programming a new rom manager from scratch. While you're at it, you might as well make one for DSi Enhanced games and even allow DSi Enhanced mode to work for such games which is theoretically possible. Say goobye to the rare and expensive iEvolution. It's theoretically possible for an R4 to use DSi Enhanced mode. You just need to program a rom manager that supports it.
hbmenu could be a good starting point for this. I have confirmed if you convert it to CIA compatible SRL that boots in DSi Hybrid mode instead of DSi Exclusive mode, give it R4 DLDI, and install it. It can access and launch things off the R4 (in DSi Enhanced mode!).
The original rom managers for the R4 don't work properly in DSi Enhanced mode however. Currently hbmenu isn't setup to launch commerical roms....For obvious reasons. The creators of it weren't interested in that. But if you got the programming knowhow, it wouldn't be difficult for you to repurpose it for that. Just don't expect the devs behind hbmenu to help, because they sure as hell won't be happy that you would ba**stardize it for retail rom loading.