Silks are not just for formal wear! There are great options that are less shiny and great for everyday shirts and blouses.
Brushed silk has a surface that is quite matt but still with that lovely sheen of silk. The brushed feel is produced by -you guessed it- brushing the surface gently with a wire brush. The feel is a lot like peach skin. Soft but luxurious. As lovely as silks such as charmeuse and crepe de chine are, they are also notoriously difficult to sew. Brushed silk is so much easier to work with since it's not slippery. In fact, it's almost "sticky" which means you don't necessarily need any pins.
Other, similar options include sand washed or sueded silk. Sand washing produces a similar matt, slightly distressed surface. It comes in a variety of washes. Sueded silk is also produced by sanding, though by dry sanding rather than washing.
Beware of the direction in which you lay the pattern pieces. The sheen of the fabric is different from different angles, therefore you should cut all pieces in the same direction. Remember also to use a fine needle and silk thread. I always hand wash my silks although I'm sure a hand wash program on your machine is just fine, as long as you use special detergent.
See how different this brushed, spun silk is next to the charmeuse. Both are lovely, but for completely different uses.