Starting to grow mushrooms

OK, I have now a fallen gum tree which is fresh, only one week old and I found an Australian supplier of mushroom cultures on Agar in petrisishes.
They cost aroud $20 and I could use feed oats. They do offer king oyster and shiitake I would prefer shiitake.
BUT then to make the grain spawn it seems to be rather difficult. They describe that you have to build a glove box and handle scary chemicals that everything is free of germs and spores, here's the link: forest fungi. We don't own a pressure cooker or a microwave either.
Isn't there something simpler? Something you could do after washing your hands with soap and on a clean kitchen bench?
It is winter here. We get up to minus 5°C but during the day it is at least 10°C or warmer.

I would love a more playful approach and I would as well like to grow some variety, because we have plenty of shady areas in our garden. BTW I cannot import any spores or spawn. I must rely on what is offered or spores from bought mushrooms.

You can use a solution of hydrogen peroxide to sterilize grain and others substrates without a glovebox or pressure cooker, although I've mostly only used it on birch dowel plugs that were being inoculated with oyster sawdust spawn. I use 3% hydrogen peroxide solution diluted to 0.3 % strength. (One part 3% hydrogen peroxide to ten parts filtered water.) I soak the birch dowels in this for about 12 hours and then they are ready to be inoculated by the sawdust spawn in a "space bag". Maybe you could adapt this method to your situation. There are a number of websites that describe this method, as well as several books.

By the way, for just a few extra dollars, you could probably just buy sawdust spawn from a different supplier in your country and avoid the problems that come with starting from agar cultures.

Not in Australia. I think there's one supplier and they want around $70. If it would be only a couple of dollars more I would go for it because it is my first attempt. The hydrogen peroxid (by the way it is used for the teeth too) sounds good because I have it at home. I want to use grain because I don't know were to get cheap wood dowels, not because I prefer grain (I plan to use the oats from the feed store).

wonder if fungiperfecti.com would ship to Australia??

That is not the poblem. Like so many awesome seeds, it is not allowed entry here - period. Or if you try you end up in jail or worse.
I do import everything that is allowed though.
This morning I was cutting up the eucalypt branches. There are very often dead brances attached to very healthy wood. This is simply the way these trees work. Is this still OK - I always cut the dead branch away. It is all from the tree which came down a week ago and the tree grew like that: healthy branch and a dead branch attached to it (can't explain that better).

As long as you only use fresh, clean, green wood without any mycelium or mold growing on it, you should be OK.

if you can't find cultures or spawn of the fungi you would like to grow, but the local markets carry mushrooms of that variety, you can try isolating tissue from the inside of the mushroom (flamed scalpel or other method) and starting a culture of your own.