you travel for less than 6 month so do not require exit permit
for NS office
if you get a valid visa from the country you starting your business
you can use that letter to apply for exit permit office
any way try to be back with your group to finish the what ever
cycle
only once a year, treat it as holiday retreat

without valid visa from whatever country you also cannot overstay
in that country. unless you plan to be para chute jumper, landed
there till get caugth by thier police then send you back.