Another crazy idea that just struck my mind is the following:

Take a look at these two sentences:

Я сражаюсь мечом.
Я делюсь радостью.

I think the tool- or means- idea behind the sword is quite obvious, but we can also treat joy as a tool for "sharing",
like I take my joy and "share" it to you

(But seriously, it's literally like I take my joy, divide it into two pieces and give one of them to you, that's why these words have the same stem, I amuse you by means of my joy)