I have 3 possible ways to explain that.
1) Eternal Manegkyou Sharingan.
The best way to avoid the side effects of the Mangekyou Sharingan is with the Eternal Mangekyou Sharingan.
What we know about the Eternal Mangekyou Sharingan is that, to achieve it, someone needs the MS of another person with the same blood (works better between brothers). Shin's clones has the exact same blood as him, so his MS might work better than a brother's in order to achieve the EMS.
Shin shows and amazing use of the MS and doesn´t show any one of the side effects, plus, the Eternal Mangekyou changes to the original designs, comes from a fusion from both brothers', Shin's clones has the same MS design as him, so if he achieved the EMS there would be no changes to the design, what leaves the posibilitie that he actually did it.
2) Hashirama Cells.
As its showed with Danzo and Obito/Tobi, the Hashirama cells are able to recharge or at least stabilize the Mangekyou, Shin was one of Orochimaru's experiment, and as we saw, Orochimaru's the one who give the Sharin-hand to Danzo. Another fact about the Hashirama cells, is that everything that used them turned white (Zetsu, Tobi, Obito's right part of the body, Danzo's hand), and Shin is as white as an Otsutsuki, what also leaves the chance that Orochimaru's gived him some Hashirama Cells to keep his Mangekyou stable.
3) His MS is just not too strong.
Compared to the Kamui, Amaterasu and Tsukuyomi, Shin's power to manipulate weapons is not the big deal, there's the chance that his jutsu didn't require too much chakra as to drain his eyes.
This theory has a contradiction, Madara's MS leave him blind despite being only useful (as we know) when it comes to give him fluidy on his moves during the fight (and use Susanoo), so this theory leaves three possible questions.
Does Madara's Mangekyou hides a Jutsu equal to the Tsukuyomi and the Amaterasu?
Does Madara's eyes start to fail through the use of the Susanoo and that's why he choose to use the Kyubi against Madara instead of the Susanoo?
Or, the principal reason that causes the side effects of the MS is the use of the Susanoo? Shin didn't used the susanoo and didn't show any signs to know how to use it. Kakashi didn't use any Susanoo (previous to achieve Double Mangekyou) but he also didn't show any syntoms of the side effects (Other than being unable to use Kamui more than once in a row).