No direct experience with Conturo glue - but every other glue/filler/whatever I ever used over the last 30 years (Cascamite, heritage horse/other animal bone glue, Evo-Stik, PVA, Titebond, UHU, epoxy, crosslinked, polyurethane, cyano plus plus plus ...) = are all 100% unstainable. The only potential way to conceal the joint is to use Unika Colorfill in the correct shade. Apply it over the glue joint, remove the excess with a spatula, wait 30 minutes, and then clean up the joint with acetone - the same process as you'd use when fitting kitchen worktops. Plan B is to use Osmo gap filler in the correct shade, cover the joint, wait 24 hours, and then gently sand/blend to profile using wet 320/400 grit automotive abrasive from Halfords.
But even after all of that - it might still not be seamless or invisible. I've had to historically resort to dabbing colour-matched paint over a joint to hide it.
I appreciate that this comes after the horse has bolted mate - but I'd wholeheartedly agree with [member=297]Michael Kellough[/member] and [member=73094]afish[/member].