Probably not. How many turns did you come up with? If +- 5 is less than about 3% of the total, I wouldn't worry about it.
Form two or five turns of wire and unwind it. Try to make the loops as large as the largest ones you took out. Divide by the number of test turns you used and this gives you length per turn. Remember, the first few turns will likely be shorter than the last in a simple winding because the wire length grows as the coil builds.
What you plan to use for slot insulation? Enamel wire doesn't like being wound directly on the iron, iron scraps the enamel off. Believe it or not, some ordinary paper (about the thickness of a 3x5 card) can work quite well. Pre-form it to extend out both ends of the slots.
Some sort of wooden/plastic tool and a small hammer can be used to 'tamp' the wires down into the slots. You'll find that getting the same number of turns of wire into the slot as what came out is a challenge. Then you need something to act as a wedge to put in the top of the slot to keep the turns in place. A variety of things can work/have been used. Everything from custom molded plastic pieces to wood strips with a paper 'cap'. Then slice off the excess paper sticking up through the sealed slot.
After the windings and wedges are in, in larger machines it is customary to coat with varnish and bake it. Then it would be ready for hi-pot testing, but you probably wouldn't need to bother with such a small unit.
When you unwound the thing, did you note carefully the connections between coils and the direction the winding enters each coil?
Is this a universal motor (with commutator) or an induction motor?
You're brave to try it. Have done quite a few in my day, and 'the devel is in the details'. Connections are a major part of getting it right. And getting the new connection splices and such to fit back into the same space as before.
In another time we used to make a wooden plate the internal size of the old field coil (Flattened out) and the same thickness as the original coil. The coil was then rewound on that 'former', counting the turns with a mechanical meter. The completed coil was then taped with cotton tape and formed to fit the field laminations, prior to tapeing of course the insulated leads were "fused" or soldered to the ends of the windings. New insulation was put into the 'slots' were the windings go and the windings installed. Once the new fields were mounted and secured with whatever method was used the assembly was dipped in varnish and baked. It is important to know the start and ends of the windings so that one field does not oppose the other in operation. Another important thing to check is the integrity of the armature, since "shorts" will burn out the fields before the armature windings in the usual case. In the case of a double insulated machine rewinding is not really practical.
Hey!!! Nice to see someone else with motor rewind experience here. Yes, we had several different coil forming machines. For AC stators it was a bit tricky getting the form to have enough 'kinks' in the end turns, but once you did, worked well. Yep, taped them while on the machine and then took them off the machine. We didn't varnish/bake them separately in AC equipment as then you can't get them into the slots without breaking the varnish.
But for 'bolted' pole type machines, yes, we varnished/baked the taped up coils (completely taped the coil with fiberglass tape on the large DC machines and AC salient-pole rotors).
Before dipping the final assembly, it was important to cover the interior faces of the laminations (or outside surface for rotors) so the varnish wouldn't build up on them. One poor guy forgot to do this one time and when it came time to insert the rotor, it wouldn't fit. The clearances between rotor and stator are *not* very large ;-)
I rewound the rotor on a Hilti hammer-drill that was given to me. It still works great after 12 years. I even had to splice the magnet wire half way through because the dinky spools of wire I got at Radio Shack weren't long enough. Go for it.