I am somewhat reluctant loosening the rigging? would this affect the mast integrity?
Petar, yes, loosening the rigging will definitely affect the mast integrity. Assuming that integrity means keeping it upright.
It actually is a good idea to exercise, clean and lubricate the turnbuckle threads once in a while. So it would be a good thing to get used to it.
With most rigs, you can remove a single shroud at a time without too much problem. Use halyards to temporarily replace the shrouds you remove.
Tape or mark the threads where they abut the turnbuckle body and you should have no problem returning the mast to the same position it's in now.