The second sentence means the same as "it is squishy". "I feel like" is similar to "it is my opinion that" and can be ignored. The sentences "It feels squishy" and "It is squishy" are basically the same. In brief, my opinion is that the answer to your question is "Yes".

The first one is a fact. You are touching the object and it is squishy. The second sentence can be an assumption you are making before you touch the object. In the second sentence you don’t know if the object is squishy, but you feel like it would be squishy, probably because of the way it looks.

We would say: 'it feels squishy' to indicate what an object feels like. 'I feel like'...refers to something that you would like...usually food.

The first phrase sounds like the speaker is more confident - they are sure the thing feels squishy. The second phrase the speaker sounds just like they "think" or "guess" that the thing feels squishy. They sound less confident.