Depending on what unit/arm/service you join, following your basic training, it might be entirely possible for you to participate in a Basic Reconnaissance Patrolling course. It's a good course, and is made available every once in awhile to reservists, mainly in combat arms/ Infantry units.
Sniper? Para? Very little chance, mainly due to course availability and requirement.
There is a very healthy shooting program underway in alot of Brigades these days, however, so you might find yourself on a shooting team competing locally, or nationally and internationally, if you qualify, regardless of arm/service. Some very prestigious shooting awards have been won by Service Battalion members, for example.
Having said that, you never know. I was always surprised at being told to submit names for the occasional 'good go' that I never imagined would be made available.
And, of course, we only nominated the best troops for those opportunities.