Viewed objectively, "I would say" implies the existence of an unstated conditional basis, which may or may not be satisfied, for saying whatever is being said. It amounts to saying "I would say X if Condition Y were satisfied," or perhaps "If I were to accept the information that I currently possess as valid and complete, I would say X." Either way, to me—and I suspect to many other people who habitually use the "I would say" formulation—the wording sounds more tentative (and less aggressive) than flatly saying "I think X."
Subjectively, however, "I would say" is now so common and is usually intended so unconditionally that it really amounts to an alternative way of saying "I think," which is precisely what you want.
My only word of caution here is that some few readers may find use of a fundamentally artificial conditional annoying. To my knowledge, the most famous critic of replacing "I think" with "I would say" is George Eliot, who considered the phrase coy and dishonest. I'll try to find the letter or essay where she condemns this usage, and (if I find it) complete this answer with that quotation. I vividly remember her hostility on this point because I use "I would say" so often—and I hate to think that George Eliot would despise my writing.
Follow-up: Here's the quotation from George Eliot. It appears in A. S. Byatt's introduction to George Eliot: Selected Essays, Poems and Other Writings (1990). I include Byatt's contextual remarks as well:
She [Eliot] was not herself afraid of clear distinct statements. There is a splendid letter [circa 1851] from her to Chapman [the titular editor of the Westminster Review, though Eliot did most of the actual editing], criticizing his style, again on grounds of illogic and inaccuracy. 'I have a logical objection to the phrases "it would seem", "it would appear", "we would remark". Would — under what condition? The real meaning is — it does seem, it does appear, we do remark. These phrases are rarely found in good writers, and ought never to be found.' As editor and essayist, she kept her own rules.
Of course, most writers have no wish to satisfy George Eliot or indeed to include her in their imagined audience of readers at all. But I think she is a reader worth having, if you can meet her demands without betraying your own voice.