I did actually have the general who's making the announcement say that those who volunteer for military service will be trained, according to their aptitudes, for less-likely-to-die positions like medics, interpreters, sharpshooters, etc. Thereby giving them an incentive to sign up. The draft is currently only taking those who graduate their equivalent of high school, since war hasn't officially been declared yet, but later, they'll draw from university students and laborers, too.
I'm gonna unpack some assumptions here:
Why is the General announcing this upcoming draft and recruiting? This implies that this government does not have civilian control of the military or any civilian government that would decide if there will be a draft or how the draft will be conduction. That's fine, as long as that is what you plan. Just looking at the assumption behind it to make sure it fits in how you structure your world. If there is a civilian government that has control over the military (whether an elected government, monarchy, whatever) it would make more sense for a civilian rep to announce the upcoming draft.
Also, the "less likely to die" positions you name, specifically "medics, interpreters, sharpshooters" aren't really that "less likely to die." In reality a battlefield medic is one of the most dangerous jobs. And if by "sharpshooter" you mean something like "Trained sniper" that's also a dangerous frontline job. Interpreters embedded with combat units are also in a dangerous job. (Now if they are back in Army HQ translating captured documents, etc, that might be different).
None of the jobs you listed would be an incentive to join early when you might not get caught in the draft in the first place. You want to use safer jobs as an incentive talk about more support jobs like clerk, truck driver, mechanic, armorer, etc. Those are the jobs that are not on the front line, that require more skill or intelligence, and are more desirable. (To any except an 18 year old who really wants to be a warrior that is). Remember even if "near total mobilization" not everyone gets drafted. Someone still has to grow the food, build the machines, run the society, etc.
Also, have thought about the training time it takes to take a raw recruit and turn them into a soldier, and then train them in a special skill on top of that? It takes months just for basic training and then a couple more months for training for infantry or artillery, etc, and up to years for people like pilots, highly skilled techs, Nurses, etc. Granted, this time can be shortened somewhat, but at a cost of reducing effectiveness. Only in the most desperate circumstances do they draft raw recruits and send them into battle with only weeks (or days) of training. We're talking about the fall of Germany in WWII type of scenario here.
And, in general, how is your military structured and what role does it play in society? Do they have a large standing military? Do they have a smaller professional army with a cadre of trained reservists to draw on when needed? Or are they attempting to build a large army "from scratch."
The answers to these question reflect on the role and position of your military in relation to the society as a whole. A very peaceful culture, especially one that hasn't faced war in generations, is going to generally have a smaller military or de-emphasis military service over a more aggressive culture (think WWII and pre-war Germany) or one that is facing constant outside threats (think Israel).
Last question: What is the point of the "The General's recruiting speech" scene, story wise and plot wise? What are you trying to accomplish with this scene. To me, the underlying scene just doesn't ring true in many ways, so I don't know if the specific answer to your question really helps you any.
EDIT: More thoughts: Having a draft is generally an unpopular thing in society. This is especially true when it is a *new* draft and the society has not had one before. It's not something a government does lightly because it causes it own problems including harming support for the war effort or govt policies.
And it takes time to train draftees and manage the expansion of the army. If you are planning a large war it makes more sense but it is also a signal (to your country and other countries) that you plan to go to war.
Does your country lack a military reserve? A common method is to require everyone (or every male) be drafted at 18 (give or take) receive a few months of basic training, and then be assigned to a reserve unit and go back to civilian life except for certain mandatory training and the possibility of mandatory call up in case of war. These reserves would be called up before any general draft as they are already trained, equipped (more and less) and can be ready to go a lot quicker.