I am so sorry to hear about Yugi - it was a great age xxx
It would be a good idea to disinfect the tank, if you don't know what he died of - but even if it was just old age, disinfecting helps remove any scent of the previous hamster.
If he didn't have any kind of infectious illness, then white (distilled) vinegar is a good cleaner and removes a lot of bugs, but not all of them. So if he did have something infectious then you'd need a petsafe disinfectant. I'm guessing you're in the US and I'm not up on US petsafe disinfectants, but someone will be. I wouldn't use bleach though.
If you use vinegar, it needs rinsing really well afterwards so the smell doesn't linger too long - which could be difficult with a 40 gallon tank! If you can get it in the shower you could shower it to rinse it out. But it might be easier to use a petsafe disinfectant that disperses easier and just needs a wipe down with a damp cloth afterwards.
This is one that is sometimes used in the Uk and it seems to be available in the US too on Amazon - it is suitable for small animals like hamsters. I think that would be the easiest option. You just squirt it on and wipe. A few days after cleaning you could wipe down inside the tank with a damp cloth to help remove any residue or scent.
Amazon.com : Clean N Safe Pet Disinfectant : Birdcage Accessories : Pet Supplies
This is another one used in the Uk that's available in the US from Amazon and it says no need to wipe afterwards as it doesn't leave residue. I would still let it air for a week or so before putting a hammy in though, so any scent has chance to wear off.
Amazon.com : Beaphar Deep Clean Disinfectant For Rodents : Pet Pest Control Supplies : Pet Supplies