Hi Jamie, welcome to Python and Iris!
You can indeed do what you are asking about, but it is done through adding a new coordinate to your cube rather than by updating the existing one. This process is adding a categorised coordinate.
Take a look at
this iPython notebook that demonstrates how to add a categorised coord (and the associated
Iris coord categorisation documentation). Note that after [4] in the documentation the cube has gained an auxiliary coord called 'year'. This contains the year value for each point in the cube's time coord. You're not limited by only being able to categorise on year either - see the documentation I also linked to for a list of all built-in categorisations - and you can also define your own categorisation function as demonstrated by [5] and [6] of the notebook.
Note also that if you meant 'can I convert the units of my time coordinate', then yes you can, so long as you're only converting the step to one of `seconds`, `minutes`, `hours` or `days`:
new_unit = iris.unit.Unit('days since 1990-01-01 00:00:00', calendar='gregorian') # define a new Iris unit instance whose timestep is days
swh_1981.coord('time').convert_units(new_unit)
Converting the units suchlike requires that you keep the same calendar, as you cannot convert between calendars; what do you do with the five days' difference between 360-day and 365-day calendars, for example?!
Hope this helps!