true, GWB would want to choose a conservative - the question then becomes when he makes a decision. My initial thought was that the Senate would choose the Vice-President, but that is entirely dependent on whether / when GWB chooses a replacement, the extent to which his choice is supported by the electors who meet throughout December as I understand it, different states at different times according to state law; the enforceability of his choice, the ability to hunt down electors, and finally the law on a dead or write-in candidate. Historically, Democrat Horace Greeley died after the election in 1872 and his Presidential votes were split several ways. Given the failure to enforce 'faithless elector' controls at various points up to 1992, the electors are free to vote whichever way they want to. Dead candidates have been elected in Missouri for example in 2002, so it depends on how the GOP want to play it.
Given that the result was clearly close - 50-50 before Jeffords switched in May 2001, the GOP might prefer not voting Cheney in and then filling the vacancy but rather agreeing on a candidate beforehand. The problem is that there is little time - Electoral votes are being certified constantly and there is little margin for error - if one state votes for Cheney or someone else, no majority is established. Furthermore, whoever the candidate is will anger someone - with little margin for dissension, the liberals and conservatives will be tempted to jockey for control.
Thirdly, amidst this you have the battle for Florida's votes. Unless Jim Baker or someone else with heft and universal party approval takes the spot, the party will turn on itself, distracting it, and GWB and Baker, from the battle for Florida. This might be enough to delay sealing the GOP victory until January, when disputes lead to mass riots (having both Presidency and Vice-Presidency subject to uncertainty and taint of corruption - neither office legitimately won by whoever occupies it or even no-one knows who will occupy it), a bipartisan GWB-Lieberman or Gore-GWB deal (relying basically on Democrat votes) that no-one expects to work or likes, or even a Democrat victory. Consider that Cheney was one of the brains of the transition and seen as the ballast that made having GWB as President safe. In the atmosphere of late 2000, anything could happen.
On the balance, I think it most likely that Jim Baker or Bob Dole would have been selected and made Vice-President, with the former a higher chance. Of course, this may have led to a Gore-Lieberman presidency though I think the legal apparatus in SCOTUS and Florida was sufficiently solid. If George tried to be his own man and picked a real conservative, sufficient electors would have blocked it, barring untimely 'accidents'.