My other half put the shoulder in the oven to cook so that when I got home I could finish it, but my food delivery hasn't come. Can I pause the cooking and go get the stuff that I need and then carry on cooking as normal? Bearing in mind that it will take me 45 minutes to come back from a shop.
In your situation, as you're just trying to slow things down and not halt it entirely, you can turn the heat down as low as it'll go on your oven, and then when you get back, turn it back to the desired temperature.
It'll throw off the cooking time enough that you'll want to use a thermometer to check for done-ness. (and it might finish in the time that the oven was set to low).