In NSW Sect.65 of the Strata Schemes Management Act (SCMA) allows an Owners Corporation (O/C) to “enter on any part of the parcel for the purpose of carrying out work ….. (that’s) required to be carried out by the Owners Corporation in accordance with this Act“, and as the work involved is required of your O/C under its obligation under Sect.62 of the SCMA to “maintain and keep in a state of good and serviceable repair the Common Property“, your O/C can legally enter your Unit in order for it to access its Common Property.
Now… that’s not to conclude that you don’t have rights to place reasonable conditions upon that access, such as perhaps requesting that cover sheets be put down and/or that all equipment and materials be conveyed to the balcony area at the one time and in your presence as opposed to on an as-needs basis, or that access be gained externally as you have suggested in your post.
So try to negotiate suitable conditions and/or alternatives for access to your balcony with your O/C, and in the unlikely event that those are unsuccessful, then simply refuse access and that will force your O/C into formal mediation and possibly to adjudication – where personally, I don’t consider that any person acting reasonably could disagree with your position.