Hi,
You need to be careful with lubricating the clock. If you just spray it like you suggested, then you are going to coat the hairspring with oil. This makes the spring 'sticky' and the spiral rings of the spring will stick to each other. The result is that the spring will act like it is shorter resulting in a much faster oscillation and therefore your clock will run much faster and also erratic so you will not be able to regulate it (ask me how I know!). Keep the spring dry at all times.
Like everyone says, oil the bearings/pivots with a cocktail stick or very very fine artists brush.
Cheers,
Bri.