FWIW I used my cheap and cheerful push fit CO2 pump as above only yesterday (when I ran over a huge unseen pothole riding in a group) and I wouldn't change it. I have seen mates fiddling around with more complex inflators before now and felt glad/smug that I'd kept it simple ;-)
I also use the smaller 12g cartridges which are perfect for one road tyre, rather than the 16g ones which always have a bit left over (and is invariably wasted as it leaks out in storage) and more suited to a MTB volume tyre.
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Simple, effective, work for me!
https://www.tyreinflators.co.uk/index.php?act=viewProd&productId=269&category=4
I also use the smaller 12g cartridges which are perfect for one road tyre, rather than the 16g ones which always have a bit left over (and is invariably wasted as it leaks out in storage) and more suited to a MTB volume tyre.
YMMV!