How Flexible Are Level 1 Runs in Dark Souls?

Can You Beat Dark Souls at SL1 using a different weapon for each boss? In Dark Souls 1 and Demon's souls, doing SL1 truly meant being stuck with level 1 stats as stat boosting gear did not exist yet. So is it even possible to beat every single boss in the game using a different weapon for each boss? Especially if we count the pyro flame as a single weapon, meaning only 1 boss can be defeated with pyromancies; and let's also restrict ourselves to only 1 shield as a weapon for a single boss encounter. Does Dark souls 1 even offer enough weapon variety on a level 1 character to complete this challenge?

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