When I used to work
for Sestrel compass manufacturers in a previous lifetime, I would have said a 4deg dip was liveable and probably less painful than doing a refill job! As others have said, re-balancing the card is not a great problem, the real problem is refilling without getting bubbles later. When the instrument was built, the diaphragm
was pulled just a little so the contents are under a very slight pressure when the plug
is screwed in and the diaphragm
released. I you don't do this, every time the temperature drops, the liquid contracts more than the compass and a bubble forms. You may then find the damping is not so good because the liquid can swish around to easily.
If you do decide to have a go, put your liquid in the freezer
for a few hours before refilling and if you can pull out the diaphragm a wee bit as well, overfill and screw in the plug
Most important, never use alcohol in the compass, only in the technician