From my understanding in a situation like this the departing shareholder should be paid at a value that's inclusive of the shares they will be selling.
But in general if shares are redeemed and the total issued and outstanding shares decrease so will the value of the company in proportion, so no change of value should necessarily occur, e.g., company valued at $1,000,000 with 100,000 shares has value per share of $10/share. If the company redeems 50,000 shares at $500,000 there will remain 50,000 outstanding shares and the company will reduce in value by $500,000 so, $500,000/50,000= $10/share
Now if the appraisers are reducing the firm's value by the future repurchase of shares and then using the weighted average you described then you'll get different math since cash & equivalents gets different weighting in each valuation method. But that's not necessarily how I'd do it (unless the situation is more complicated than I read) because the value of cash in the various valuation methods is taking in all sorts of assumptions whereas the book value method described above supports these types of transactions by keeping the relationship between the company's cash to it's value pretty straightforward.