Publishing a paper without supervisor
On one hand, you seem to have a research advisor who is quite supportive of you; he has already offered you a post-doctoral position when you finish.  On the other hand, you are concerned that he tends to attach himself to, and take credit for, work on which he is only peripherally involved.  This places you in something of a quandary, since your advisor has not made a meaningful contribution to your paper.

However, I would suggest that you show your advisor the paper to get his feedback.  Even if that feedback is not useful in terms of the content of the manuscript, your advisor probably has a good understanding of how papers should be written, and where they should be submitted.  Moreover, when other scholars are evaluating work done by graduate students, you are not going to be significantly penalized for having your advisor as a co-author.   Having a paper that is co-authored by your advisor, but with you as the first authors, is not going to be perceived as that different from  a single-author publication.

Perhaps your advisor will make some useful comments, but he will decline to be an author on the paper.  (This happened to me, in my interactions with my advisor, more than once.)  You seem to think that your author is not likely to be magnanimous in this way, which is, in the abstract, unfortunate.  However, as I stated above, having you advisor as a co-author is unlikely to be counted against you in a significant way, and maintaining a good relationship with your advisor (for whom you man continue working as a post-doc) can be extremely important for a future research career.  So I do not think that you have much to lose by showing your paper to your advisor and getting the advantage of your advisor's guidance.