Does buying just enough shares to get control change what I'm exposed to?

Buying enough shares for control — generally just over half, though the exact threshold can depend on the corporation's own governing documents — changes your power over the company, not the underlying liabilities themselves. The corporation's debts, contracts, and legal exposure are the same the day after closing whether you hold 51% or 100%; what control gives you is the ability to direct how the company responds to them.

The nuance is that control can cut both ways. On one hand, you can make decisions unilaterally — settling a dispute, changing management, restructuring operations — without needing a remaining shareholder's agreement. On the other hand, having control also means the remaining minority shareholders may look to you, as the controlling shareholder, to run the company fairly and in the corporation's interests, and Ontario corporate law gives minority shareholders remedies if you don't.

If control is your goal, it's worth having a business lawyer confirm what threshold actually gives you the specific powers you're expecting under the corporation's articles and any shareholders' agreement, and what obligations toward remaining shareholders come attached to that control.