dnd 5e – Can a sorcerer summon an improvised weapon as his covenant weapon?

I'm brainstorming about a character concept, a tavern fighter who brings together a variety of random elements that are usually found in a bar (just because he is more familiar with those than normal weapons) He will be a Hexblade Warlock Level 3 with Pact of Blade and will have the Tavern Brawler feat.

I intend to use the third option of the Tavern Brawler feat to fight against enemies hit by my covenant weapon:

When you hit a creature with a disarmed blow or improvised weapon on your turn, you can use a bonus action to try to attack the target.

Tavern Brawler requires me to hit with a makeshift weapon, so I intend to invoke, for example, a kitchen knife, a bottle or even a roller or a pan, just for hilarity. And yes, the character will be a female dwarf innkeeper.

So, can I use Pact Weapon to summon improvised weapons? Or is it required that the Pact Arma be a conventional weapon? Can it be a kitchen knife that counts as a dagger and improvised weapon?