This was fun, I liked the concept. Taken further you could have a viable project on your hands here.
I think if you took out the timer though it would make the game both easier but also more engaging. Being able to take your time get yourself into a good position would be good for the player.
Also I think if you increase or remove the weapon despawn rate that might be good as well as I found myself having to drop weapons earlier in order to collect a new one before it despawned on me and I lost it forever. Regardless I thought it was a very fun game.