There is a possibility of being blissful without being wise, but that blissfulness is not true blissfulness; it is simply what people call happiness. It comes and goes, it is momentary. And it always leaves you in deep frustration and despair. The cost is too much and not worth it.
There is also a possibility of being wise without being blissful, but that wisdom is pseudo and false. It is what is known as knowledge. It is borrowed, it is a burden. Anything that has not arisen out of your own experience is always a bondage. It can nourish your ego, but it cannot reveal yourself to you. The true seeker has to find bliss and wisdom together. And both can be easily found together because they are like the two wings of the bird, meditation.
Meditate: on one hand you become blissful and on the other hand you become wise. Both grow simultaneously in a kind of deep synchronicity. In the ultimate state, bliss becomes wisdom, wisdom becomes bliss.