There is a very limited list of items generally prohibited for importing (like drugs, alcohol, and firearms). You may check the components of items you're planning to send to see if there's any prohibited component within.
My personal opinion is that with the items you listed, you're all fine, just care about any alcohol component.
Here's the exact list of items prohibited for importing, but it is in Ukrainian, and each item refers to its particular article in the Ukrainian Classification of Goods for Foreign Economic Activity (Українська класифікація товарів зовнішньоекономічної діяльності, УКТ ЗЕД).
In any case, make sure you declare all the contents of your shipment on your paperwork. If you believe that your goods may need permission to clear customs, be sure to contact Ukraine customs before booking your shipment or ask your Ukrainian friend call the Contact Center Department of the State Fiscal Service of Ukraine - Tel. +380 (800) 501-007
The rest depends on your carrier's rules. Here are some to consider:
Alternatively, I have a very positive experience with Internet shops who would buy cosmetics in Europe, deliver it to Ukraine, and send it locally to your door. Their fees would be higher than normal parcel delivery (say, +20-25% of the item's price), but it frees you up from any paperwork, and there's no risk of damaged/stolen item because you pay when receiving.
