Hi Jim,
The short answer is that yes, you probably can do that with no special considerations-any 18 size American movement would likely drop right in.
Here's the longer and more complete answer:
Waltham made 18 size movements in seven different models: the 1857 model, 1859, 1870, 1877, 1879, 1883, and 1892 models. The 1859 model is irrelevant to our discussion as it was only made in keywind and faded into obsolescence in the 1860s.
Of the remaining models, several have some special casing requirements.
The 1857 model, as a stemwind watch, was only made as a hunting case movement. The stemwind versions of these have a male stem on the movement(requiring a female stem in the case). The set lever is a bit of a different configuration from that typically seen on later watches, and requires a fairly wide slot as well as some special clearance in the bezel in order to fit.
The 1870 model, like the 1857 model, when made in stemwind has a male stem also. These actually came with a couple of different setting mechanisms, including button setting, nail setting, and lever setting. The button and nail set versions are not readily adaptable to a case not made for them. The lever set versions operate similarly to the 1857 models, and carry the same considerations.
The 1877 and 1879 models have a set lever the same location and width as a "standard" lever. Most of these movements, however, have male stems on the movement that require a female stem in the case(some do have female stems on the movement). Incidentally, all 1877 models wind at 3:00(or are keywind) and all 1879 models wind at 12:00.
The 1883 model is the most common Waltham 18 size model, and shares casing characteristics with most of its contemporary 18 size watches from other makers. The stem and set lever configurations are the same. It's worth noting, however, that nearly all open face 1883 model movements are stem set, whereas all 1883 hunting case movements are lever set.
The 1892 model is a bit of a different breed but will fit any case that the 1883 model will fit. The better grade open face 1892 models(Vanguard, Crescent St, 845, Appleton, Tracy & Co) tend to be lever set, whereas the mid grade ones(PS Bartlett) tend to be pendant set when open face. Early open face 1892s tend to all be pendant set(pre SN 7.5 million or so). All hunting case 1892s are lever set.