No, "vaikuttaa kasvua hidastavasti" is fine. Google "hidastavasti", and you will find lots of hits, and always with "vaikuttaa ... hidastavasti". I have no idea how to explain the rules for it (well... count me as native), but it means that something is causing or affecting the growth rate to slow down (or um... in a growth rate slowing down way). So, in the linked
English article we have "It is believed the drugs interact with cancer cells to slow tumour growth.", and in the
Finnish "Ibuprofeenia sisältävät tulehduskipulääkkeet voivat vaikuttaa syöpäsoluihin niiden kasvua hidastavasti, tutkijat arvioivat.". So, both sentences leave it a bit open what is excactly slowing down the tumor growth, but Ibuprofein is somehow involved.
"Ibuprofeenia sisältävät tulehduskipulääkkeet voivat hidastaa syöpäsolujen kasvua, tutkijat arvioivat." Now, this is "Ibuprofein can slow down tumor growth"... close, but not quite the same meaning. The actor here is more direct in its action.
Ibuprofeenia sisältävät tulehduskipulääkkeet voivat vaikuttaa hidastavasti syöpäsolujen kasvuun, tutkijat arvioivat. Well... to me it leaves it a bit open what word "hidastavasti" here is moderating. I do get it what it means, as the word is hidastavasti, and so it must mean that it is slowing the growth. But as you could also have "vaikuttaa nopeasti syöpäsolujen kasvuun" which means that it acts fast, it kind of makes my mind go "um, or did I read that wrong... did they mean that it is affecting slower and slower to the growth... or, um...". When you have "hidastavasti" last it really is no other way to decipher than it's affecting the "syöpäsolujen kasvuun <millä tavalla>".
Ibuprofeenia sisältävät tulehduskipulääkkeet voivat vaikuttaa syöpäsoluihin niiden kasvua hidastaen, tutkijat arvioivat. This is the closest, in my opinion. Just a slight different meaning in how I see the action happening, but it means more or less the same. Um... like here it's "Ibuprofein can affects the tumor cells to slow down their growth" vs. "Ibuprofein can affect the tumor cells in a slowing down the growth way". So, a "what does ibuprofein do" vs. "what is the effect on the cancer cells".
But well... that's just what my ear says, no idea if it is correct or not.