I dont think a liquid cooler would work there. The small size of that case is limiting and Installing an 120mm aio, the largest that would fit, would take up your only 120mm spot, likely adding to your current problem. 120mm aio liquid coolers arent the best either.
You may be able to use a smaller air cooler like a cryorig c7, that is almost guaranteed to fit and deliver good temps. Here is one for 33bucks.
https://m.newegg.com/products/9SIA4UF39D5213?ignorebbr=true&source=googleshopping&nm_mc=KNC-GoogleMKP-Mobile&cm_mmc=KNC-GoogleMKP-Mobile-_-pla-CRYOSTORE-_-CPU+Cooling-_-9SIA4UF39D5213&gclsrc=aw.ds&gclid=CjwKCAiAy-_iBRAaEiwAYhSlAymm3BAQeFD_LuNkNskcA5VNFe29Dw3vp1d8gKg_1RdWif7rty7f4hoCWsIQAvD_BwE.
What temps are you seeing and what cooler do you have? Anything under 75-80c will not hurt your pc at all. The stock wraith spire cooler for the 1700 shouldn't cause that issue unless its air starved. This could be the case, but hp could have used a cheaper cooler, which isnt uncommon.