If I may add my two-cents. To Recap;
Each Arkentool is related to a 'rare' unit.
The Arkenhammer with Dwagons
The Arkenpliers with Uncroaked (Decrypted)
and The Arkendish with Archons
In addition each Arkentool is best wielder by a non-royal unit. Stanley was a Warlord when he found and attuned to the Arkenhammer. Wanda was a Croakamancer Caster. Charlie is presumed to be a Thinkamancer Caster. Now as Casters are seen as the antithesis to Warlords my assumption is that the fourth Arkentool would likewise best attune to another non-royal Warlord (hinting at Parson).
If we assume Parson and that the fourth Arkentool is related to a unit he has synched with, I see three possiblities; Twolls - Parson's friendship with Bogroll early on as well as his attempts to relate with Zhopa indicate a possible connection. There's also the fact that Twolls specialize in Fabrication. (Propsed tools that can relate with Twolls - Arkenwrench, Arkenallenkey, and Arkenlathe, three very multifunctional tools. Arkenwrench and Arkenallenkey follow the Even Simpler (funny shaped sticks), while the Arkenlathe falls with the Missing Step Theory).
Secondly, we have Casters. In strictest sense, they are a unit and are extremely rare when it comes to popping. Parson has exibited Caster abilities himself, and has formed bonds with many Caster across different fields; Sizemore the Dirtamancer, Wanda the Croakamncer, Misty the Lookamancer, Jack the Foolamancer, Maggie the Foolamancer, and has made an impression on Charlie the (purputed) Thinkamancer as well as Caster's in the magic kingdom especially Janis the Hippiemancer. (Proposed tools in relation, Arkenwelder (I dunno), Arkendice, Arkenwiki - Save the welder, all deal with higher levels of capability as well as understanding that Erfworld is essentially a game. Arkendice follow the Even Simpler train of thought (a block), Arkenwelder follows the Missing Link Train of thought, and the Arkenwiki indicates that they have superceaded everything (if it exsist's it has been wikied somewhere).
Thirdly, we have the yet unintroduced Daemons. Little support, but looking back at the arrival of a volcanic region as well as the descruction (sacrifice maybe) of the Sword of Ruthelessness into the lava could segeway into Daemonic territory. (There's also the fact that there is no real counterpart to the Archeons yet). Plus, if we go with the classic portrayal of Demons in the Real World, wouldn't they want nothing more than to 'break' everything. (Proposed tools in relation, the Arkenshovel, Arkenfork, Arkensaw. This takes a little more leeway, Arkenshovel obviously because 'Daemons are underground' you've heard the drill. Arkenfork. This theory is three-fold. The tool is a pitchfork, an actual tool used to bale or pitch hay, is also associated with Demons, and is a possible counterpart to Charlie's plate. Finally there is the Arkensaw, this tool banks mostly off of the pun, but also serves as an analogy to Charlie's Plate. The Arkenshovel (unless a largw powershovel, would conflict with the Arkenhammer in terms of complexity. The Arkenfork follws the Even Simpiler, beig a pointed stick. The Arkensaw could either be a reforged serrated blade (using the Sword of Ruthelessness) sticking to the even simpiler, or a jigsaw (as an electric carving knife) supporting the Missing Link.
Personally, I'm a believer that the Fourth Arkentool is going to be the Arkensaw, weilded by a Warlord.
Going with the Missing Step theory stating that the fourth Arkentool requiring a degree of complexity involving springs, gears, clockwork, steam, or even an engine, it would appear that the Arkensaw doesn't fit this mould. However, this in normally because most assume a handsaw design. Their are mechanical saws, three of which come to mind, circularsaws, jigsaws, and most importantly, chainsaws.