I think you may have trouble with some of the larger petrels - especially with them vomiting fishy oil all over you - which is their natural defence - but the (black and white) storm petrels are really tiny and should not be too difficult to handle

During night-time bird ringing (banding) sessions at coastal headlands during the breeding time in Shetland I have been lucky enough to have Storm and Leach's Petrels in my hands. They are not really much bigger than say a swallow.