Handsaws are a little too common as it is right now. If a player has two or more handsaws, it's way too easy to die, and wasnt an uncommon occurrence from what I saw. This is especially irritating in Round 2, where players get 3 instead of 4 health for some reason which makes the issue all the more confusing.
The intoduction of lobby settings for having more autonomy of how the game is played would alleviate this issue to some extent and would be a cool idea anyway. That, or a tiered item system where items from the box are given a tier and you may only draw 1 tier 2 item, 3 tier 1 items or so forth. Handsaws, based on their power with the default low health would go in tier 2.