If you make picks out of broomstick and nails a few notes on their construction:

The portion of the nails sticking out needn't be very long. Too long and they are more difficult to use. About 3/4", plus or minus a bit, is plenty.

Whatever portion is outside the wood you need about twice that inside the wood. It won't do to have the nail pull or break out sideways. Pre-drilling the holes for the nails is good because it makes placement more exact and easier, can help reduce splitting. The hole should be roughly one-third the nail diameter in softwood and two-thirds in hardwood. Small barbs pinched into the steel near the non-working end with dykes are an option that will help keep the nail in place.

The portion of the wood rod holding the nail should be firmly wrapped to reinforce the wood and prevent splitting. Remember your hauling your body weight and waterlogged clothing out on a thin bit of steel shoved into the end grain of the wood. Wood that is going to want to split at the worse possible moment. Wire or stout fishing line are good.

Self recovery picks are a good, simple and quick woodworking project. With a few basic skills and a couple of hand tools it is pretty easy to produce a very workmanlike pair in about an hour. Less per unit if you produce them three or four pairs at a time. It is a nice evening project that you can work on with spouse or kids. But remember that those picks your building are life saving devices. So build them like your life depends on them.

As an aside they also have a small roll in self-defense. A friend of a friend's daughter was accosted and only got away from the attacker when she pulled out her pick and drove it into the back of the man's hand several times. Police were able to arrest him when he showed up at the ER. They made the case on that but a detective noted that his blood was also on the nail so DNA evidence was an option.