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It's not too difficult.
This is a good guide
I would always recommend using a heatproof matt to go between pipe and walls / back of cupboards. It saves potentially very costly fire related boo-boos.
Out of curiosity, when you say compression fitting, are you talking threaded compression olive ones? If so, you could consider push fit pipe fittings, which are the easiest and great for tight spaces.
How hard is soldering copper pipe? After wrestling with compression joints all evening yesterday I did, in the end, finally have the dishwasher plumbed in but I feel like learning to solder would have made the job a lot easier.
And we have a sink with a big strainer, are they standard sizes? I ask because it has a food waste macerator attached to it which we don't want and is leaking from within the unit itself so I need to remove it and fit a new trap/waste pipe and maybe a new strainer if the existing one is integrated into the unit below which it looks like it could be.
Ideally I just want to swap it out for a new one with standard BSP thread to fit a new 40mm trap/waste which I can connect up to the existing waste pipe.