How to beat the entirety of Resident Evil 4 without the Merchant's help. This means you will mainly rely on your handgun, shotgun, and much later the free Broken Butterfly (you will not have room for the rocket launcher).
Guide to Complete without the Merchant
Part 1: Village
The village portion of RE4 is fairly easy. Avoid fights when you can, use the shotgun on large groups of enemies, headshot and kick when possible, knife as much as you are able. The knife will save you ammo, which will come in very handy later on.
Part 2: Castle
This part is a bit more challenging then the village, but the same advice applies to this area. Often, enemies will have Plagas come out of their heads. Destroy them with the shotgun or a flash grenade, if you have it (I highly recommend you save them for this).
Some parts are extremely difficult without the help of the Merchant: the hedge maze, both Garrador fights, Salazar, etc. I promise you all of these are beatable with only the starter weapons and the Butterfly (do not miss it!).
Now, at last we come to...
Pretty much the same deal as the first two areas: avoid fights as much as possible, knife enemies as much as you can, use shotgun on large groups of enemies.
I do have one more tip that will be of great use to you: the Ladder trick. Climb up a ladder, stand at the top, and start swinging your knife. This will help you to defeat large groups of enemies, and it saves ammo.
"But how do I defeat the Regenerators?" I hear you ask. Fairly simple: blow off a leg, avoid getting bit, and knife away. Eventually, it will die, even the Iron Maidens.
The Krauser fight is fairly simple. Use the knife on him (this does take some practice).
For the U3 fight, run and pray for the first part, use the Butterfly, shotgun, and explosive barrels for the second.
Note: No need to stress if you die.
Finally, we come to the final boss, the Man behind the slaughter, Saddler. Simply use your guns and the girder levers. Grenades work especially well, if you still have any.