Re: No swapping in weapons from your inventoy in a fight and poisons become instant-spells with a shared cooldown-timer
Preventing weapon swap entirely is not the way to go, however, there should be some cost to it. Such a change would however not represent an intended balance change but a fix to a flawed game mechanic with balance implications that may or may not have to be addressed.
The simplest and to me most sane way would be to add the base weapon delay of the new weapon to your current swing timer (or starting it) on weapon swap. This would make applying multiple poisons a tradeoff and not a clearly superior thing and it would remove the currently perfectly valid 2h + shield swap abuse: hit them with your 2h, swap to shield while in swing delay to take advantage of your shield spec without any downside, swap to 2h again once out of swing delay and repeat, effectively making you wield 2h + shield.
A different poison mechanic, namely like live does it these days, would be nice and also horrible, it would be nice for assassin players as it is primarily a qol but it would also be horrible as it dramatically lowers the barrier of entry making assassins even more prevalent. At the same time giving out these skills at specific evenom specs while ignoring + from items or rr, as it would be actual skills granted at different spec levels, would have huge spec implications and remove a major benefit assassins gain from higher rr.