Your thought processes are on track - the primary electrical impact is on the RF resistance of the wire.
Twisting the wires effectively creates a larger wire diameter with more surface area. The additional surface area reduces the RF resistance attributable to skin effect. Depending on the frequencies involved, this may be of minimal benefit. Based on the geometry of your antenna, it appears that you are in the 130 MHz range. If so, the radiation resistance of the antenna is around 70 ohms which means it would take at least of couple of ohms to have a significant effect on efficiency. The formula for antenna efficiency is:
$$Efficiency=\frac{R_r}{R_r+R_l} \tag 1$$
where Rr is the radiation resistance of the antenna and Rl is the resistive losses in the antenna.
Efficiency is multiplied times directivity to specify the gain of the antenna.
One thing to consider is that corrosion between the individual strands can offset the increased surface area. We often see this when a coaxial cable gets water inside the jacket. The braided outer conductor becomes corroded and it no longer makes an effective shield. But since mechanical strength is your primary reason for twisting the wires, this will probably have negligible impact on the performance of your antenna.