I've done this plenty of times, skipping the isolation entirely.
Isolated the scope earth, checked the correct plug position (It's reversable in EU) and used neutral as scope ground, so the potential between scope chassis and earth is basically non-existant (maybe 5-10V), this way you won't be shocked.
Of course safety first, check everything twice, and measure ac voltage between scope chassis and earth to be completely sure.
Also fixing the probe into 10x with some tape to prevent accidental switching / potentially blowing the channel.
Call me whatever but it seems pretty simple to me.
Anyone considering copying DavidAlfa, should note that
Neutral is regarded as a Live conductor.
Line is the obviously hazardous live conductor, with full supply voltage on it, but you are only one failed Neutral connection away from the supply voltage becoming present on Neutral. Its rare, but people
have been electrocuted by failed Neutrals putting dangerous voltages on things they thought were safe to touch. The fault doesn't even have to be on your property - it could be anywhere between the wall socket and the utility company's distribution transformer, which may be streets away.
The risk is obviously higher for someone in a low rent apartment building in a (relatively) poor country in Europe than for someone in rural North America in a single family property with recently inspected wiring and its own 'pole pig'. Eliminate all exposed grounds on or near your bench, and stand on an insulating mat and you can reduce the remaining risk considerably
TLDR: Floating your scope is still dangerous even if David is happy with the risk of his Neutral going 'hot' while he's using the scope!
To our O.P: Ground the <expletive> UPS so the scope is grounded, and don't put the probe ground clip on nodes that have significant voltage with respect to ground. If you cant ground it properly (e.g. aircraft, moving vehicles), ground it to the airframe or chassis, but you need to understand "equipotential bonding".