TransTechnology Corp. of Alexandria, a manufacturer of aerospace-defense products, yesterday announced a tender offer for Breeze Corp. Inc of Union, N.J., a producer of helicopter rescue and cargo equipment.

Under the terms of the friendly bid, TransTechnology would increase its share of Breeze's outstanding common stock from the current 12.6 percent to 49.87 percent through the cash purchase of up to an additional 299,000 shares. The company is offering $24 a share. Breeze, traded on the American Exchange, climbed 2 1/2 on Wednesday and closed yesterday at 23, unchanged.

In a second stage, TransTechnology plans to exchange 2 1/2 shares of its common stock for each share of Breeze that is not purchased in the tender offer. If TransTechnology stock is selling at less than $12 a share at that time, however, the merger may be canceled at the option of Breeze. TransTechnology traded at 10 1/4 Wednesday and closed yesterday at 9 5/8, down 5/8.

The announcement was made jointly by Arch C. Scurlock, chairman of TransTechnology, and Joseph J. Mascuch, president of Breeze. Scurlock would be chairman, Mascuch vice chairman.

For the year ending this March, TransTechnology earned $3.7 million ($1.26 a share) on revenues of $151 million, up 35 percent from $2.77 million ($1.17) the previous year. The company has plants in Maryland, Pennsylvania, Massachusetts, Rhode Island and California.

Breeze had net income of $2.5 million ($3.26 a share) on sales of $34.3 million during 1981. In addition to hoists, winches and controls, Breeze produces security and law enforcement devices, hose clamps and electrical cable assemblies.