If you keep the solution in a tightly sealed container, it should not be a problem.

Salt solutions have specific equilibria with water in the vapor phase, which depend on the nature and concentration of the salt. In fact, % humidity in closed containers can be set to specific values by including uncovered salt solutions. There are tables that give the relative humidities of various salt solutions.

The vapor pressure above the concentrated electrolyte solution is pS = pW*exp( - nu*Mw*osm ), where pW is the Clausius-Clapeyron vapor pressure of pure water, nu is the isotonic coefficient, Mw is molar mass of water, osm is the osmolality of the solution (osmotic coefficient times molality; you can take it from any handbook, e.g., CRC).

If the vapor pressure in the ambient air is pA < pS, the concentration of your solution will increase with time. If the vapor pressure is pA > pS, then the concentration decreases with time. Only when pA = pS, concentration remains constant. However, at normal humidity of 50%-70%, even for saturated solution, water will normally evaporate from the solution. Except you reach really high concentrations (e.g., 10 mol/kg). Or you have a freak electrolyte - TlNO2 can reach pS ~ 50% at ~ 1 mol/kg.

But since evaporation is equally bad to hygroscopy, and besides pA varies a lot, you need to keep the solution closed.

The hygroscopic salt will absorb water from the atmosphere even if it is already in solution. Basically, solution is the interaction of solute particles with the solvent (water in this case). So if the solute is hygroscopic, it will absorb water vapour even if it is in a concentrated solution to attain equilibrium of water to solute particles. Keep the solution in a tightly closed container. Alternatively, you could keep the anhydrous salt in a tightly closed container and prepare smaller stock volumes of solutions only when needed instead of preparing a stock to use over a time period.

Aqueous solutions of hygroscopic salts may either uptake or lose water. It depends on the temperature and relative humidity of the atmosphere above the solution. The concentration and temperature of the aqueous solution (close to surface) determines the relative humidity for an equilibrium atmosphere over the solution at the same temperature, so that neither mass transfer of water nor heat transfer would occur. A closed atmosphere tends to closely match this case. If the atmosphere is not in thermal and/or chemical equilibrium with the solution, as may be the case with an open atmosphere not submitted to environmental control, heat and mass transfer should occur across the solution surface. That may result in either dilution of the solution or in its concentration (if not already saturated in the salt).