Unlike DoT fluid, mineral oil is not hygroscopic. So your “aged” shimano brake fluid should be fine.
If the fluid that comes out is black/dark and you’ve got enough fluid it’s worth doing 2 full bleeds.
I’ve also found if you leave the brake lever tied on, it encourages air bubbles up to the top of the system. I tend to leave mine “on” for an hour or so. Before i snip off the cable ties I tap the caliper, and then up the brake hose to the lever. I usually get a number of smallish bubbles come out then and the brake feels a lot better. You can also slightly undo the lever clamp (with the pot atached to the lever) and roll it back and forth -+45 degrees whilst flicking the lever to encourage any bubbles out.