Word for delaying a decision with only one option?

If there is only one course of action, then there is not really a decision to make, so this is a case of

• delaying

  Postpone or defer (an action)

• stalling

  Stop or cause to stop making progress

• procrastinating

  Delay or postpone action; put off doing something

• dragging one's feet/heels

  Be deliberately slow or reluctant to act

• deferring

  Put off (an action or event) to a later time; postpone

If there's a chance that the situation will change between now and when action can no longer be avoided, you might say

• hedging

  protecting oneself against financial loss or other adverse circumstances

If you want a word with a bit of color to it, you might try filibustering or stonewalling.

Those both include the additional notion of blocking something, not just of avoiding it, which seems to be what the OP is requesting.

Other verbs besides those previously mentioned in other answers include dawdle, bide, and tarry.

However, there is no sense of inevitability here, or of something that has no other possible course of action. I’m not sure it makes sense to have a word for avoiding a “decision” with only one “option”. It doesn’t seem like much of a decision if there is no choice involved, nor can something be an option if there is but one of them.

It’s a bit like trying to avoid death or taxes: sure, you might be able to file for an extension, but these things only go so far. :)

I think to procrastinate implies laziness, avoiding a duty, and that's not really the sense I got from the question. In my mind, the best way to express the idea asked for is with the phrase 'to delay the inevitable'.

If forced to express this idea in a single word (though I don't know why that would be the case - a strict word limit?), I'd probably opt for the verb to temporize: to behave indecisively or evasively in order to to delay acting.

The word you want is stalling.