At the time of the trade, the 1% would be determined and split between both parties. Trade at 1 BTC, fee is 0.01 BTC and 0.005 is charged to each party. Buyer buys 1 share for 1 BTC & 1.005 BTC is removed from their trading account. Seller sells 1 share for 1 BTC and 0.995 BTC is added to their account.
That would be a 1% fee split between buyer and seller. EDIT: I would imagine you would round any remainders down to the nearest 0.00001 BTC.
My personal opinion on how trading fees should be handled:
The fee should only be charged to 1 party, but not limited to 1 side of the trade. The person providing the liquidity should be able to make their trade for free. For example, if I put up a buy order at .15 and a sell order at .16, but the stock is actively trading at .155, I should not have to pay fees when my orders are eventually filled. The person who chooses to fill the order (buy at .16 or sell at .15) would pay the fee. This would encourage more open orders and improve liquidity. Just placing the fee on one side or the other seems to encourage holding or discourage trading, while free trades for providing liquidity would encourage more people to list orders, thereby encouraging more trading. It would also allow companies to list their IPO without being victim to double dipping (charging to create the asset and then charging to sell the asset).