Note: Many of these articles are very old, and although the technical information is still relevant the equipment mentioned may not be (for example a Stormy cooker was state of that art in 1995, but not in 2021).
Going from leashes to nothing at all can result in dropped tools, both because you’ve become accustomed to letting them drop and because you’ve yet to get into the habit of securing your tools when out of your hands. The best way to overcome this is to attach the tools to yourself in some way at first, either removing this connection once you become confident, or retaining it when on climbs where a dropped tool could spell disaster. Personally I’ve dropped both tools in the space of about 20ft already, with one going all the way to the bottom of the face so, personally, I tend to keep them attached much of the time.
The two best options are to either use an elastic lanyard like Grivel’s Double Spring Leash (£24 I think this may be discontinued but you can still buy them in some shops), clipping it from your harness to your axe’s spikes, or make up two shorter lanyards which can be clipped to your rucksack straps. On many axes that feature removable hand hooks, some modification will have to be found in order to clip in the lanyard (BD, Charlet), as these hooks often block up the clip-in loop at the bottom. This can either be done by drilling or filing and tying a loop of 4mm cord through the hole, which although far from ideal is the best that can be done at the moment (come on manufacturers why don’t you think of these things?).
When making your own lanyards make sure they are long enough to give you adequate reach, without being so long as to get tangled up and keep them as separate coloured lengths of cord (5mm), so they can be more easily identified and untangled and make sure the cord is long enough to allow you to stow the axe on your harness. To make untangling easier have a mini wiregate karabiner at each end, allowing you just to unclip from them if need be.
These loops are NOT designed for resting on - only to secure your tools and there is an inherent danger in attaching the axe to you via the spike, in that it will hang spike first - potentially harpooning you in a fall. It’s for this reason that you should never let the tool dangle, but either clip it to your harness, or hook it on your shoulder.