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I have not used a mini digger before but how hard can they be?
Re: pipes etc, it's a new build that I'm pretty certain doesn't have anything under the back garden. All our services run from the front and through our street.
Soul-
If the soil is as soft as you say it is, that will chop out in no time with a spade. And if' you're only going down 150mm, most of that will come out as sods. Chop a line where you want the edge and just lift big chunks as you go. See if your neighbours want any free turf. Back when I used to have a proper job as an archaeologist, you could open a trench that size in a morning easily. Certainly quicker than it would take to arrange, bring in and get to grips with a mini digger. Although, nowhere near as fun. Sods are much easier to move a lot of spoil quickly than loose earth.
stevo_com
So long as you know you've got nothing under it, I'd say that's reasonable (assuming you've used a mini digger before, or had more than 3 go's on the coin operated static ones at theme parks).