If Gai does it, then it's possible.
If it's possible, then you can do it.
... Well, maybe not as well as the infamous elite Jounin, but you have the option on the table. You just need to figure out how to do it.
...
Not much comes to mind. The Academy students are all tested to see if they can touch their chakra at all, and while you were spared that by dint of being a member of a famous ninja clan, meaning it would be foolish to suppose that you couldn't touch and use your chakra, you know the process.
You sit down on a bench and focus.
Within a few minutes, you start to feel the fire inside of you. Warm, pulsing with life, and gently suffusing your whole body, from the core outwards to the inside of your skin. Centered, as befits a Doujutsu user, not only in the brain, belly, heart, and lungs, the four main nodes of thought, fuel, life, and breath, but also in your eyes.
It's all very interesting, but for what you're doing...
You try forcing a little out.
... It isn't easy. Your chakra is stable and contained in your body, and it does not want to leave it. It's slow to move. Painful, almost. No, not almost. Definitely painful. You're doing something your body isn't supposed to, it's like trying to bend a joint backwards. Possible, but...
And when it does move, the little bit that you were trying to move spurts out all at once, almost stirring the air in a physical puff that sets Saki flinching.
"Did you just force chakra out of a tenketsu?" she asks, uneasily.
"Yeah, maybe?" you reply.
Saki gives you an uncomfortable look.
"... Don't kill yourself." She finally says, seeming to have weighted a lot of possible responses and carefully selected her words. "Ninja have a lot more chakra than we need to live, but we still need it to live."
Yeah, yeah.
You barely pay any attention as you bring Saki back to the Hyuuga compound, and then head home yourself. And then... then you get to quietly training.
It's hard. After the first night, you are exhausted enough that you just sleep through all of the academy classes, ignoring bits of chalk bouncing off your head and quiet checks to reassure people that you hadn't just died in the back of the classroom without warning. Which has apparently happened, a student that thought they were a lot better with poisons than they actually were, and with a foolish understanding of how resistances were gained.
It's at the second day that you finally gain headground, and manage to force a little bit of chakra partially out, but not completely out of your grasp.
You're hanging on to the fragment of chakra outside of your body with what feels like the tips of your fingernails. The slightest slip, the faintest jostling, and the energy is gone. Dispersing freely into the environment around you, and unable to be retrieved. Or used, in any way.
... fingernails aren't the best way to put it, but the only other metaphor you can think of is disgusting. The tenuous grip you can keep on the chakra, not quite lost to you...
It's like taking a massive, painful shit. Stopping in the middle, and just holding it.
It's hours after you first think of the metaphor before you can pick up another attempt at it, and what you manage is shaky.
It takes a lot of concentration, to hold chakra like this. Most of it, in fact. You find yourself moving through life on autopilot, the absolute minimum attention devoted to the real world, all the rest of it wrapped up in holding chakra with invisible fingertips.
And frequently slipping, losing hours and hours of work in an instant.
Weeks pass, to little more effect than to leave a cloud of chakra hanging invisibly around you like a cloak, and disturb your sleep trying to work out a way to keep hold of it while you rest, because otherwise it's just thrown away uselessly again as you fall asleep and let go again.
It's really all a crapshoot, like trying to hold a secure grip on a knife while you sleep. Sometimes you manage to keep hold of nearly everything, other times it all goes away and you wake up needing to begin from scratch again.
... It's exhausting, and you don't sleep well from the effort. But you have to get the basic ability down before you can work out things to do with it. And so you go through all your classes in a dull haze, relying on your sharingan to memorize the lectures so you can go through them and read the instructor's writing and lips to piece together what it was about.
This continues until, in the lunch break of an unremarkable day some number of uncounted days into the training, you're confronted by Hinata of all people. The most timid wallflower of the Hyuuga.
And she's in your face for some reason.
"Y-you have to stop." she stammers, trying her hardest to be authoritative and failing hard, fingers trembling. "You're making, you're making yourself sick!"
"... I'm fiiiine." you reply, the word stretching out as you strangle off a yawn.
"Y-you look like you haven't slept in a week!" Hinata insists.
You've slept. Not... great, but that's how it goes. You wobble a little and let your eyes focus again, then unfocus them as your attention reverts to keeping a grip on your cloud of chakra, invisible to everyone else. Who doesn't have a doujutsu. Huh. Does Hinata see it?
You wave a bit of the chakra cloud in her face and she flinches. A slow grin crawls across your face as you wiggle more of it.
"Stop it!" Hinata insists. "You're hurting yourself!"
---
[ ] "Ssssssso?"
[ ] "Yep."
[ ] "Make me."
[ ] ??