Spanish Cedar Wood:Cigar Humidor Wood Of Choice..
Not entirely without risk, but if the bleeding really gets excessive, you can try provoking it to bleed out in an oven.
Put the box in the oven and then slowly heat it to 70°C (160°F) Start cold. Leave it there for about 24 hours and wipe the bleeding stuff away every once in a while. (Careful, the dry air in the oven won't feel all that warm, but the 70°C sap will burn you). Leave the box into the oven while cooling down again.
After this treatment, the wood will not tend to bleed anymore as long as below this temperature.
The sap itself is not disastrous for cigars. in fact, the sap is what gives Spanish Cedars its typical aroma.

Hope this helps,
Bart.