It's concerning that you think the point of a share buyback is...

It's concerning that you think the point of a share buyback is for a company to manipulate its stock price to be higher. The actual point of a share buyback is for a company to buy its own shares at a price which the company feels is lower than the intrinsic value of the shares so that the valuation gap will close over time, and the company will make a return from this. The company is not supposed to go ahead and close the valuation gap by forcing the stock price higher!

Any buying or selling, in theory, has an impact on the stock price, no matter how small. However, generally accepted principles are anything up to 20% of volume are reasonable, but in reality, most companies stick to around 5-15%. 87% is unheard of.