Is there a way to put the Nvidia Shield to sleep and also wake it with the same button?

Below is the remote I'm using, One for All URC6810.

 

To be honest I'm not sure. On the other hand, there's really no real reason why you would need to do that. Just leave it woken up. There shouldn't be much difference in power consumption, as even in the sleep state it is still powered (for example it needs to maintain RAM content and also the CPU is still active so it can react to some events).

I don't have Shield TV, but I have Xiaomi MiBox with Android TV and I don't use its sleep mode at all.

I need to have the Shield power on & off (sleep) with the same one button as the tv does because in my house that's a scenario that makes more sense to people.

Currently all white buttons work for the tv perfectly (which makes sense to people).  So when I have to explain that the black power button will turn the Shield off (really asleep) but that same button will not turn it back on again (really waking it up), it creates confusion will folks.  This is why I need it to work from one button -- to make things simple.  

I can't tell you if what you want to do is possible or not, but I see an issue with the setup you'd like to have:

If you could put it on the same button you use for your TV, then there's a risk that it'll desynchronise. If the signal won't reach one of the devices (for example the remote is held at an angle which would cause the signal not to reach ShieldTV/Flirc) and you only turn on your TV without waking the ShieldTV, then the next time you press the button you'd wake the ShieldTV but turn off the TV at the same time.

But anyway, I'll repeat what I've said in my earlier post: just don't turn off your Shield TV at all. Leave it woken up. Using sleep mode doesn't affect your power consumption so using sleep/wake just complicates things for you and you don't gain anything from it.