If I believe a name is worth (say) £5,000, do I ask for 0.6 Bitcoin, or do I make an allowance for price drops or increases? I don't want to quote the price in US dollars or Sterling.
If you don't want to mention fiat at all, nor do you want a thrid party payments gateways, then set up a small website and put the price though blockchain's API:
https://www.blockchain.com/api/exchange_rates_api
For example:
https://blockchain.info/tobtc?currency=GBP&value=5000
Even if the price goes from 0.6 to 1.2 or 0.3 you can be sure that the buyer will always make the BTC<>fiat math in is head, we all do
This is for the case you want that person to know at each time what the value of the website is in BTC without you having to do the maths each day, but if you're negotiating through email for weeks, maybe months, what you're planning on doing will turn into a headache for the customer, and maybe for you too.
Why should volatility be problem?If you are so afraid of the Bitcoin price fluctuations,than why not just sell your bitcoins for fiat,right after the buyer pays you with BTC for the domain name(after 3 confirmations).
He is concern that he will start negotiation at 1 BTC for example as he values the domain at 11k and by the time all the deal is getting done which might take a few weeks the prices would have changed and he needs to tell the client the prices has gone up to 2 BTC as BTC dropped to 5k or the client will get out of the deal since 1 BTC is worth now 50k.