How can I improve my search effectiveness early on?

Wisdom doesn't affect Searching, as far as I know. So I'll instead cover how you can improve your searching, rather than improve wisdom. The main things that affect it are Luck, having a pair of lenses, and getting Excalibur.

• Luck is the main factor. The higher your luck, the more likely you'll find a door in fewer chances. If you have slightly bad but not horrible luck, you can usually guarantee finding a door in around 20 tries. But if your luck is really bad, it's incredibly difficult to find such doors. So more important than anything, don't ruin your luck. If you have ruined your luck, you should wait for the bad luck to time out before you continue to search.

  To improve your luck, the main options are to throw gems at co-aligned unicorns or to sacrifice monsters that make your god happy. These both rely on the fortune of running into an early co-aligned unicorn and altar respectively. As reinforced by sepp2k in the comments, do note that good luck will time out just the same as bad luck, if you lack a luckstone. Which, early game, is not a very common prospect.

• Lenses are an accessory time item you can wear over your eyes. They're extremely rare, but if you're lucky enough to find a pair early on then you can use them to help, as they improve the success rate of finding secret doors. There is an artifact pair of lenses, but they are Neutral alignment (and the Monk quest artifact, specifically) and so wouldn't be of use to a Lawful character such as yourself. But they are a pretty handy item for Neutral non-monk characters lucky enough to get an early wish that they would like to spend on it.

• Excalibur is an artifact longsword. Any Lawful character who reaches XL 5 can dip a longsword into a fountain and have a chance to get this weapon. As a Lawful Valkyrie, you start with a longsword, which makes this that much easier to get. Plus, it's a great weapon to have in general.

  While wielded, it not only grants the searching extrinsic (which automatically searches at the end of every turn), but it also improves your success rate. Note, however, that the bonus it gives is in proportion to its enchantment level. So if you don't happen to run across any scrolls of enchant weapon early game, it won't help too much. But this weapon represents one of the best early game aids to searching.

If you have good item fortune, then you may also come across a wand of secret door detection or a stethoscope. These items, once you find yourself at a dead end, greatly expedite your success by simply revealing the secret passages. Healers start with the latter.

First of all unless your luck is really low, you can assume that when you have searched 30 times and not found anything, there isn't anything to be found. As an interface note you can type 30s (or n30s if you have numpad enabled) to search 30 times, so you don't actually have to press s 30 times (and it will stop searching when a monster interupts you).

As for increasing your wisdom: other than potions of gain ability or blessed potions of enlightenment, the most reliable way to raise your wisdom is probably to exercise it by searching a lot (though the search has to be successful so don't just hit s a thousand times at a place where there's nothing to find as that won't do anything).

Though as Grace Note points out raising your wisdom won't actually help you in searching.

Another way to increase your chances of finding hidden doors and traps is to get an item that grants auto-searching like for example Excalibur. As has been mentioned in the chat, lawful characters can get Excalibur by dipping a long sword into fountains once they're at least character level 5.