Glad to hear Huntsman I am not the only person who often uses stuff wrongly - until a sudden light bulb moment. Holding a running chainsaw at the wrong end a few times was particularly uncomfortable
I do use the turn and twist cage but just pick up the queen by the wings and drop her in. You might reasonably ask if I am going to do that, why don't I just mark her in the hand there and there? The reason is a held queen will often attract workers to investigate and I prefer to move away a bit from the flying melee to mark and to allow the paint to dry a bit before release. If she is under a cage or in a plunger tube there is less of a chance of me messing up and dropping her away from the hive in the long grass.
For clipping, unless i got lucky with a stick out wing when marking, I do hold her in the hand but always with nitrile gloves on, so the greasy and smelly fingers you mention neither contaminate her nor attract interest from workers. I have mentioned before that the old advice "you can't clip queens with gloves on" dates from the era of thick leather gloves as the only available option. I have not used them for many years.
You can very definitely pick up and securely hold queens with nitrile and even marigold type gloves. The dry rubbery surface actually helps grip the queen with minimal or no finger pressure applied - the very slight desensitisation from nitriles is actually helpful in that you do not distracted by workers landing on your hands or even attempts to sting you. If you do all you beekeeping with bare hands anyway - fill yer boots.
As I mentioned above in the thread, the advantages of clipping are a whole lot more than just allowing you to take slightly longer intervals between inspections. Another benefit is doing splits. If you get it wrong and end up with a queen in a part which raises queen cells or they are deliberately already present, no worries - they may indeed attempt to swarm but you won't lose any workers as long as you inspect normally and respond accordingly. You can also do splits without finding the queen if she is clipped, by deliberately leaving a protected queen cell surrounded by foil in either part, as long as you follow up to remove any additional emergency cells. Not recommending it, just saying it is possible. If you don't protect it, there is a chance that the reduced population in the queen right part will simply knock down the cell and you end up with old queen, which you may or may not want.