You're assuming companies must operate at a fixed profit level and have price setting powers--most do not.
Consider the opposite scenario--if we suddenly lowered corporate taxes to zero. Would corporations pass these savings along to consumers by lowering prices and increasing wages? Perhaps to some degree, but in a non-monopolistic market, prices are dictated more by supply, demand and competitive pressures. Companies may use the extra money to pay down long term debt, invest in property, plant & equipment or pay larger dividends. The interest rate and credit environment will have a large effect on what they decide to do.
The larger driver of wages is competition in the labor market. Companies will pay as little in wages as they are legally able to while still finding suitably skilled employees. Simply having more cash on hand is not an incentive for a company to raise its wages across the board.
Raising taxes on a profitable competitive corporation doesn't directly affect wages, it reduces their profits.