Have your Shield Disabled

There are 5 main ways that you can get this goal. To craft a shield you need 1 iron ingot and 6 planks of any kind (can be Nether wood).

Piglin Brutes

Piglin Brutes exclusively spawn in bastions, and Draftout guarantees a bastion near to 0,0 in the Nether. Brutes can spawn in set locations in 3 different situations.

Firstly, they can technically spawn wherever normal bastion Piglins spawn, but on a lower chance (10% Brute, 80% Piglin, 10% nothing). The second case are the normal Brute spawning places (e.g. in ramparts, especially triple chests, or next to lodestone chest in bridge etc.). These are weighted 83% Brute to 17% sword piglin (or a bit more to brute if the wiki is wrong), meaning you are highly likely to find brutes in these areas. Thirdly and lastly, there are guaranteed Piglin Brute spawns, which are confined just to the Treasure bastion. In bottom treasure there are guaranteed brutes, as well as on some of the wall pieces. There is also 1 guaranteed brute in the right (double single chest) rampart in Treasure. Brutes are always hostile to the player, so all you have to do is hold up your shield and wait for it to be disabled, and turn and run before the brute finishes you off. 

Piglins

Piglins can be found in bastions (as above), in Crimson Forest biomes with 33.3% spawn weight, and in Nether Wastes with 8.93% spawn weight. 

Sword piglins will always switch to a golden axe if they pick one up, since its base damage is higher than their sword. Piglins will always prefer crossbows and spears to golden axes, so if a crossbow piglin or a spear piglin picks up your axe, they will not equip it. You can kill them to get the axe back, but a better option is to punch any piglins who look like they might steal the axe from the sword piglin you threw it towards. Piglins in heavy aggro will not get distracted by gold items, so they won't pick up the axe. 

Once a piglin has equipped an axe, their attacks will disable shields. You don't have to wait for the Piglin to finish observing the axe either. If you punch it as soon as it picks it up, it will auto-equip it and start using it to hit you.

Vindicators

Vindicators can either be found in Woodland Mansions if you have one, or more realistically spawned in Raids after entering a village with the Bad Omen status effect. Vindicators are not guaranteed until wave 2 of a raid, but if you start the raid in normal or hard mode there is a chance in wave 1. Find a vindicator and have them disable your shield. You can use the village bell(s) to give the raiders glowing, and you will be able to tell from their outline where the vindicators are (and if there are any). 

Wardens

Wardens might be less feasible than the others on this list so far, but their melee attack (not the sonic boom attack) will disable shields. There are some obvious drawbacks to this method compared to the others, but some boards might reward it (e.g. kill warden and no easy nether enter). 

Zombies etc.

By far the least reliable method is relying on the fact that Zombies, Husks, Zombified Piglins and Zombie Villagers have a chance (if spawned in Normal or Hard mode) to pick up gear, which includes Axes (even wooden ones). The problem is that the chance depends on local difficulty, which in draftout is likely to be on the lower end (given that the number of days is below 3 and the time spent in 1 chunk is likely to be low), which is around 7% on Hard mode, or 1 in 14 zombies. You can turn it to Hard and drop an axe around some Zombies or Husks, but bear in mind that you would be getting lucky if it works. If you are going to force this, it will be best to be on a low render distance and repeatedly hit zombies to force reinforcements (0-10% for normal Hardmode zombies, 50-85% for leader zombies, which have around a 5% chance of spawning). This can get hairy quickly with baby zombies, especially while being on hard mode.