I HIGHLY advise that you go in practise tool to train cancelling the second auto attack from passive because this build gives attack speed which makes it even harder to do compared to more classic akshan builds.

Just try to farm and play safe against assassins, against weak 1v1 and easily abusable champions, just go for it and do what you have to. Use your Q to poke since it's range increases the more enemies it hits and use your w to roam if you can.
Be careful as akshan really lacks base stats and hence doesn't have a lot of burst potential early in the game, prefer poking your enemy and all in him when he has 1/3rd to 1/4th of his hp left.

Since you are a marksman / assassin, you're an easy target so be careful not to go in mindlessely. The goal of this build being to be as fast as possible, your goal is to cancel the second auto attack from passive and get bonus movement speed instead making you really hard to catch as long as you can attack first. When you get a kill, use your e to reposition yourself or chase low hp targets. Use your w to stay hidden and wait for your team to engage before popping out of the shadows and killing their backline, it's basically like playing twitch, but you are faster.
Of course, try not to die and hit as many people as you can to revive your allies.