I do not think any of the Rings were intended for Men or Dwarves. LoTR is a bit ambiguous on this issue. In
The Shadow of the Past Gandalf tells Frodo as follows:
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The Three, fairest of all, the Elf-lords hid from him, and his hand never touched them or sullied them. Seven the Dwarf-kings possessed, but three he has recovered, and the others the dragons have consumed. Nine he gave to Mortal Men, proud and great, and so ensnared them.
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In
The Council of Elrond it is stated only that the Three were hid by Celebrimbor. So from LoTR it is clear that Sauron gave at least the Nine to Men, but how the Dwarves got the Seven is not clear.
In
Of the Rings of Power and the Third Age, it is explicitly stated that when Sauron first put on the One Ring the Elves were aware of him and took off their Rings. Sauron then demanded that all the Rings be turned over to him. When Celebrimbor refused, war ensued and the Three were borne away and hidden.
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But Sauron gathered into his hands all the remaining Rings of Power; and he dealt them out to the other peoples of Middle-earth, hoping thus to bring under his sway all those that desired secret power beyond the measure of their kind. Seven rings he gave to the Dwarves; but to Men he gave nine, for Men proved in this matter as in all others the readiest to his will And all those rings that he governed he perverted, the more easily since he had a part in their making.
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So the Three, the Seven and the Nine were made and held by the Elves (made with Sauron's aid as to the Seven and the Nine) for their own use and the Dwarves and Men were given them by Sauron to give them "secret power beyond the measure of their kind."
The Three were made to preserve and heal and enhanced the power of their bearers to do so. The precise purposes of the Seven and the Nine are not known, but presumably, to some extent, they enhanced the natural abilities, power and desires of those who bore them. Thus the Dwarves who bore them became even more wealthy and skilled, for example, but being perverted by Sauron they also enhanced the Dwarves' natural tendency to be greedy as well.
Could the Three Dwarven Rings that Sauron recovered have been used to make more Ring Wraiths? Pure speculation, but perhaps. We don't know when Sauron recovered any other than Thrain's Ring (T.A. 2845) but that is said to be the last of the Dwarven rings he recovered. Sauron entered Dol Guldur around T.A. 1100. It seems as if he would have plenty of time to create new wraiths, assuming he could do so. Maybe the "secret powers" of the Dwarven rings were simply not suited for this purpose. Or maybe Sauron kept them to gather their power to himself.