If it is a trailing marrow there is no problem with stopping the sideshoots by pinching them out or cutting them off.
If it's a bush plant, make sure you don't cut off the growing point where the new marrows form, but you can judiciously remove some of the larger leaves to stop it encroaching on surrounding plants etc. Inevitably this will make the plant less vigorous but removing just some of the leaves shouldn't affect the marrow much.
If you are growing them for a 'largest marrow' competition, then definitely don't do it!
Coincidentally I've just removed about half of a courgette plant growing in the polytunnel as it was growing over tomatoes and pepper plants. I'll tell you later if it still goes on producing courgettes!

Well I do have enough plants to go for it and trim, and others to leave, also going to dig the plant as a whole and move one onto the compost where I hear they can grow well, the other into a new position.
Have also trimmed courgette.

Will let you know.

Alex