This seems obvious enough. Don't want to use your ammo? Don't use guns. Most of the enemies may easily be defeated using melee weapons, as most enemies are melee focused, and are the most common enemy to find such as: Null Bodies (Orange guys), Crablets (Headsets), and most Zombish (corrupted grey guys).

The best melee weapons seem to be Sharp based weapons, instead of Blunt. These include Knives, Cleavers, Crowbar, Axes, Spiked Bat, Swords, and One Handed Hammer. Crowbars and One Handed Hammers are both Sharp and Blunt based melee weapons, depending on what part of the weapon hits the enemy.

A good strategy for defeating Crablets is to hold your arms or melee weapon in front of your face so when they jump they get blocked and/or damaged. Using your hands allow you to quickly grab them and slam them against a surface for the kill, or using a sharp weapon may impale them to it for easy grabbing, or even instantly kill it if it jumps eye first. The fastest way to kill a Crablet without using melee weapons is to hold them, then run fast into a wall to ram it. Will surely kill them in one hit.

Though there are many melee focused enemies, and are the most common to fight, there are still three enemy types that can hinder and melee only run: Clean Up Crew, Box Turrets, and Zombish (With projectiles).

The Zombish that have projectile attacks are not too hard to deal with, as their projectiles are slow enough to be dodged, and most often hit their allies instead. You should consider targeting them first whenever they are present with other melee focused enemies. It's best to run with melee in hand to increase the power and force of your melee weapon to quickly kill / knock down the Zombish. You can tell if its dead if its projectile hand stops glowing.

Box Turrets are probably the least common enemy, however placed in spots that are difficult to get around without shooting them out. If available, a Trashcan may be worn on your body to be used as armor to block all bullets as you proceed to or around it, however seeing will be difficult. Also a Trashcan Lid may be used as a Shield as it can completely block bullets, or if put against your face could make the turret believe you're an object.

The main enemy type that is the real issue is the Clean Up Crew (aka guys with guns).
They don't appear often, but when they do they come in great numbers. They are capable of killing you quickly when in close proximity, making melee combat a hard venture.

In my experience, the easiest and safest method of dealing with the Clean Up Crew is to use One Handed Weapons, and a Shield if available. One handed weapons such as the Lead Pipe, various Knives, and the Cleaver can one hit kill Clean Up Crew enemies if hit on the head (the strength required is debatable). The only Shield items I have been able to find are Trashcan Lids, they are capable of completely blocking bullets from the Clean Up Crew.

It is best to run to each one and hit them in the head in quick succession, or run past them entirely if possible. If you go into a dying state, you can try to quickly kill one of them to regain health and continue your assault / escape. A Trashcan can also be used as armor if available.

After playing through Story Mode again, I have made some helpful observations.

#1: Clean Up Crew are possibly the weakest enemy in the game. I have found out that you can one hit kill the Clean Up Crew with a single punch to the head, or two depending on strength. This makes it even easier to kill them in rapid succession as your fists are the most easily maneuverable, cost effective, and accessible weapon at your disposal. It is recommend to keep a constant sprint as you race to each one.

#2: The seven only Box Turrets that get in the way are easily avoidable. The first one in level Streets is easily avoidable as you can climb the wall in front of its range and sneak behind it. The second one and third one in streets guard ammo so its best to use a trash lid to block bullets as you get behind them. The forth one in the level Train Station is avoidable using the vents to get to the room its guarding and get behind it, and the fifth one in the elevated Rail Car behind the door to the front car can be rushed behind before it can attack, allowing you to get the ammo boxes behind it. The sixth and seventh one in the level Tower can be avoided by taking the right side's left path that leads to the end level trigger during the final Clean Up Crew confrontation.

#3: Zombish that have projectiles will not use projectiles when within melee range, making them easily beatable with melee combat.

#4: Clean Up Crew on the level Tower that roam the store areas are very unlikely to attack you. They have the lowest detection range of all enemies, and are more busy dealing with the Zombish that also roam the area. This makes it easy to collect the ammo in the area, and navigating the area, especially since its when the most Clean Up Crew are present in the game.

If you're missing around 300 bullets for the Nimbus gun, you can grab the extra bullets in the chamber above by blocking off the lift with the nearby seating, or use the gravity cups to climb up the side to prevent the lift from rising and blocking your way back. There should be a few boxes of ammo on both sides of the chamber. Jump back down to put it in the Monomat. There are also two boxes of ammo on the walls in the Monomat room at the sides, both walls can be climbed to reach them.

You may comment additional information that you may think should be added, strategies, and any mistakes I may have made. I will make changes as i make new discovers while I continue playing the game myself. This is my first guide so be kind.