We-e-ell. Dollarisation, that is simply allowing your favoured currency (in the case Sterling) to circulate as a means of exchange, can and does happen. Of course it isn't normally the way a European democracy goes about things. It could happen in Scotland's case, but it won't. But Gem is quite right, anyone could do it, and there's nothing stopping a post indy Scottish government doing it if it wanted. (Other than the damage it'd do to its reputation etc).
Your point b) is a possibility. Scotland could have its own currency, pegged to Sterling. Pegged currencies are fairly common, but if market speculators think the rate is wrong, the pegged currency would be vulnerable, as Sterling itself was when it was part of the ERM (which was a pegging mechanism). But many currencies have been pegged to Sterling, especially former colonies. (Indeed, during colonial times, the Sterling zone was maintained this way to facilitate trade within the Empire). You set up a currency board and maintain Sterling reserves equivalent to the domestic currency that is circulating (1:1). That's how the Isle of Man, Gibraltar and the Channel Islands do it now. But that isn't a currency union, for currency union you need a single central bank and a single currency. That is what Salmond and Swinney propose, rather than a pegged currency.