I turn the shoes upside down at an angle, (the shoe opening pointing towards the ground with the sole at about a 45 degree angle) and I literally pour Lexol on the underside of the tongue so it acts as a slide for the conditioner into the shoe. Then I just get my hand in there and blindly wipe it on the ball area of the upper lining and everywhere else. It does a good job of absorbing everything just using your hand. If it doesn't you can just shove an old t shirt in there to absorb the rest. I don't over think it really, doing this is better than doing nothing. I then put the trees back in so that should absorb extra as well.
I would be careful doing this on shoes that use gemming. If you get too much conditioner in there and it seeps in between the insole and upper lining it can loosen the glue that holds the gemming in place causing it to shift when you get a resole.
Thanks on the edge dauber suggestion!