Yes; just show your Delta status card at the check-in desk (to get extra baggage allowance) and at the lounge entrance (to get lounge access), while firmly explaining that you are switching to Flying Blue so you do not want the agent to change the FFP number in your booking.

For benefits that require having your number in the reservation - such as access to a greater selection of (reduced/free) seats, for example - you will just have to forego those particular benefits. You will not get the "SkyPriority" flash/logo/legend printed on your boarding passes, so in places where this is checked via scanning your boarding pass, you will have to forego SkyPriority. However, if it's a location where a human is manning the priority entrance, again showing your Delta status card in combination with your boarding pass should be enough (but may not be). You could also, of course, consider buying tickets that have SkyPriority included as part of the ticket, particularly where this would lead to you achieving status in Flying Blue more quickly.