For starters, I would leave out mention or use of the word "dig". I notice that's the way you phrase it in your very question here, for example. Instead, you're asking permission to "metal detect". And THEN if the subject comes up via casual conversation, you can address that by saying "... and you won't even be able to tell I was here", or "I'll leave no traces", etc...
Yes I know this semantics subterfuge is sort of odd, if you're working small front yards of manicured turf. Because, doh, how are you supposed to ... uh ... discreetly "dig", when you made no mention of digging (like if they're watching you now through the window, etc...). Here's how I've handled that: When I start, I make sure to PURPOSEFULLY go for a shallow dime or quarter or tab or something first. Something so shallow I can pop it out with nothing but a few pokes with my screwdriver. After doing that for the first 4 of 5 signals (and showing them the boring dime or tab, etc..), they will invariably get bored, go back inside and .... THEN you go for the deeper ones.
But if you're talking just acreage like in cow pastures, farms, lots, etc... then .... it's probably a moot point.