No. I know he had his own ideas on spelling, some at least being adopted, but I've not seen a "list." I have a republished version of his original 1828 American Dictionary of the English Language, and in that he spells "duel" duel.
NOAH WEBSTER URGES REFORM OF SPELLING (1789) From Noah Webster, “An Essay on the Necessity, Advantages, and Practicality of Reforming the Mode of Spelling and of Rendering the Orthography of Words Correspondent to Pronunciation,” Dissertations on the English Language: With Notes, Historical and Critical, to Which is Added, by Way of Appendix, an Essay on a Reformed Mode of Spelling, with Dr. Franklin’s Arguments on That Subject (Boston. 1789). pp. 391. 393-98. 405-6.
It has been observed by all writers, on the English language, that the orthography or spelling of words is very irregular; the same letters often representing different sounds, and the same sounds often expressed by different letters. For this irregularity, two principal causes may be assigned:
1. The changes to which the pronunciation of a language is liable, from the progress of science and civilization.
2. The mixture of different languages, occasioned by revolutions in England, or by a predilection of the learned, for words of foreign growth and ancient origin.
* * *
The question now occurs; ought the Americans to retain these faults which produce innumerable inconveniencies in the acquisition and use of the language, or ought they at once to reform these abuses, and introduce order and regularity into the orthography of the AMERICAN TONGUE? Let us consider this subject with some attention.
Several attempts were formerly made in England to rectify the orthography of the language. But I apprehend their schemes failed to success, rather on account of their intrinsic difficulties, than on account of any necessary impracticability of a reform. It was proposed, in most of these schemes, not merely to throw out superfluous and silent letters, but to introduce a number of new characters. Any attempt on such a plan must undoubtedly prove unsuccessful. It is not to be expected that an orthography, perfectly regular and simple, such as would be formed by a “Synod of Grammarians on principles of science,” will ever be substituted for that confused mode of spelling which is now established. But it is apprehended that great improvements may be made, and an orthography almost regular, or such as shall obviate most of the present difficulties which occur in learning our language, may be introduced and established with little trouble and opposition.
The principal alterations, necessary to render our orthography sufficiently regular and easy, are these:
1. The omission of all superfluous or silent letters; as a in bread. Thus bread, head, give, breast, built, meant, realm, friend, would be spelt, bred, hed, giv, brest, bilt, ment, relm, frend. Would this alteration produce any inconvenience, any embarrassment or expense? By no means. On the other hand, it would lessen the trouble of writing, and much more, of learning the language; it would reduce the true pronunciation to a certainty; and while it would assist foreigners and our own children in acquiring the language, it would render the pronunciation uniform, in different parts of the country, and almost prevent the possibility of changes.
2. A substitution of a character that has a certain definite sound, for one that is more vague and indeterminate. Thus by putting ee instead of ea or ie, the words mean, near, speak grieve, zeal, would become meen, neer, speek, greev, zeel. This alteration could not occasion a moments trouble; at the same time it would prevent a doubt respecting the pronunciation; whereas the ea and ie having different sounds, may give a learner much difficulty. Thus greef should be substituted for grief; kee for key; beleev for believe; laf for laugh; dawter for daughter; plow for plough; tuf for tough; proov for prove; blud for blood; and draft for draught. In this manner ch in Greek derivatives, should be changed into k; for the English ch has a soft sound, as in cherish; but k always a hard sound. Therefore character, chorus, cholic, architecture, should be written karacter, korus, kolic, arkitecture; and were they thus written, no person could mistake their true pronunciation.
3. Thus ch in French derivatives should be changed into sh; machine, chaise, chevalier, should be written masheen, shaze, shevaleer; and pique, tour, oblique, should be written peek, toor, obleek.
4. A trifling alteration in a character, or the addition of a point would distinguish different sounds, without the substitution of a new character. Thus a very small stroke across th would distinguish its two sounds. A point over a vowel, in this manner, a, or û, or i might answer all the purposes of different letters. And for the dipthong ow, let the two letters be united by a small stroke, or both engraven on the same piece of metal, with the left hand line of the w united to the o.
http://edweb.sdsu.edu/people/DKitchen/new_655/webster_language.htm