Actually, the guns reload (recharge) independently. You can do exactly as you suggested: hold the fire button (LMB) and switch between 1 and 2 on the keyboard. That way, you can fire multiple projectiles when both weapons are recharged. This is actually an important technique to use in order to progress through the harder waves.
Regarding the recharge time of the second weapon — wait for the Power-Ups that increase the fire rate. :)
I thought about adding some sort of recharge icon near the reticle itself, but I think it might be too distracting and could make the UI feel a bit too heavy or busy. You do have the recharge bar at the bottom left, though, which indicates the recharge progress as well as the fire rate (e.g. 1.0/s = 1 projectile per second).
I do have a small question: if you’re playing on a Windows machine in the browser, does the crosshair look alright? Or is it too thin or too small? Is it readable enough?
Also, does itch.io give you any issues when switching to fullscreen?
Thank you