For armor, I don't remember anyone welding extra plates on ships, but people do weld torpedo bulges on ships since they don't have to be structurally integrated into the armor to work.
I've only gone through the RN starting ships in detail so far, but there were some armour improvements to the armour of the older Kent class as well as to HMS London, in refits that took some time, using cemented armour to improve the belt. A number of the Queen Elizabeth class got improvements to their deck armour as well (with at least one of those rebuilds finishing after 1936). It did happen, but it was quite unusual, and would be more trouble than it's worth putting in the game unless there was a detailed 'rebuild' mechanic.
On the upgrades that took place between 1936 and 46 (RN ships that were there in 1936 only - just because that's all I've got the data easily on to hand, but as the older ships are also good examples for what was/wasn't upgraded):
- The vast majority was AA, radar or ASW.
- Some of the AA increases were quite substantial - most of the earlier RN cruisers had 1-barrel 4in DP mounts, and most of these were upgraded to two-barrel mounts before or not long after the war started. To give an example, in 1936 HMS Rodney had 6 4" DP barrels, 16 2-pounders (two octuple mounts) and eight 0.5in Vickers guns (two quad mounts). After her 1944 refit, she had the same number of 4", but now had 44 2-pounders (five octuples and one quad) and 68 20mm Oerlikons (58 single, five double mounts).
- Even the smaller ships had upgrades - every RN destroyer that survived past late 1941, more or less, switched out its Vickers guns for 20mm Oerlikons, and usually the 20mm armament was increased again later in the war. Even the 1927 SS Oberon received one 20mm Oerlikon during the war.
- ASW was increased in pretty much every destroyer, with all receiving more depth charges and depth charge throwers, and many receiving Hedgehogs later in the war.
- Radar was added to every ship of CL and up, with BBs (even the Revenge class), but I haven't come across radar being added to the old DDs, even though the smaller vessels built during the war, even DEs, had a decent amount of radar equipment.
Most of those old WW1 BBs and BCs had already been upgraded with new engines (and some with armor) prior to the time frame of the game. There were not very many upgraded withing the games time frame (though there were a few). As previously stated upgrading the main guns was almost impossible unless the ships were designed for the bigger guns in the first place (Mogamis) or had the barrels re-bored.
The Japanese and Italians did a few major refits of their BBs and CVs (Japan only), and a number of these either finished or started after the start of HoI4. For example, Kaga was reconstructed between 1935 and 1938, with the reconstruction involving the lengthening of the flight deck from 624 feet to 817.6 feet, while the Japanese Ise class battleships were rebuilt finishing after HoI4 starts, with the rebuild involving an increase in the weight of armour (by the look of it mainly improvements to deck armour) from 9,525 to 12,644 tons. These two BBs were then converted to hybrid BB/seaplane carriers in 1943, with the removal of two main armament turrets, the building of a short flight deck and hangar and a removal of their main anti-ship secondary armament (but not their DP AA guns).
