I did something similar with our last hamster Charlie when he became very old and had walking difficulties. He also seemed to appreciate it and even perked up a bit sorting out the house and making a nest.
It's hard when they get so old. You may find some days he makes the effort to get favourite treats and some days it's just too much of an effort. Or he may have toothache as well
I used to put some baby food in a little egg cup pushed down into the substrate a bit as well as the hard food and Charlie loved licking up his baby food. Age four months is usually fine as it tends not to have onion, tomato and spices which aren't good for hamsters. Pumpkin and chicken was Charlie's favourite. I found latterly he didn't like eating porridge or scrambled egg off a teaspoon as it seemed to be an invasion of his space when I put the teaspoon near his nest so just leave things nearby and he'll take them if he wants them. But if a bit of scrambled egg on a teaspoon tempts him out to eat some then I'm sure he'd enjoy it
They seem to carry on with their little routine and habits until they literally don't have the energy - which is nice that they keep being hamstery and taking care of themselves. Also why it's important to keep putting the regular hard hamster mix out so they can pouch and hoard it - they do that even if they're not eating it - it's their routine and activity. I used to put the hard dry hamster mix in the usual bowl and some extra in another smaller bowl (sometimes a baby food lid) that had been soaked in a tiny bit of boiled water so it was softer. If you put the water on when it's boiling it soaks up easier and quicker - and then leave it to cool completely before putting it in the cage obviously! I also used to use another baby food lid and put 2 or 3 broken up science selective biscuits in that - soaked - he loved those.