I doubt that weapon tech is able to go "slower" than "other" tech. Inventions in metallurgy that are needed to build complex machines would certainly have an impact in weapon design too.
Even if no better weapons are available the war would be much different from for example the napoleonic wars.
railroads allow mass army movements
steamships allow fast movement around the globe
better quality steel allows "Body armor" (rerise of Knights?) that actually is not too heavy and still is able to withstand musket balls.
self propelled vehicles: Mount big shields in front and your infantry moves up to the enemy without being in danger of being hit by enemy fire (no indirect fire weapons except "mortars"
(Short) swords, axes and so on might be choice weapons as you can't be hurt from a distance, so melee is the only way to fight effectively.
The problem is: without modern weaponry the defensive measure improvements that OTHER technology allows will render "muskets" obsolete. Either you develop better firearms or you have to think of other ways to hurt your enemy.
When it was possible to build metal ships the existing gunnery was suddenly not able to even scratch the better armed ships (The Monitor, Battle of Lissa). In the battle of lissa they used the ships to ram the enemy (like in ancient times) to win the battle. Offensive guns soon caught up with armor. So as long as one field of tech develops other fields have to develop too.